Why is the FBI making such a big deal out Hillary Clinton's personal email server?

They aren't presently.

Or at least, they don't appear to be anymore, even with recent events.

They were doing their job by investigating the issue, which was then a "big-deal", but they completed their investigation in July, stating:

no charges are appropriate in this case -- FBI Press Release

At present, that statement is still the official position of the FBI.

Update:

Since originally posting this answer, recent events in relation to the emails the FBI was reviewing in respect to an investigation into Mr. Weiner have concluded. The FBI reported that no new relevant emails were found, and their previous conclusion still stands.

In-fact, NBC reports that nearly all of those emails were actually duplicates.

A senior law enforcement official confirmed to NBC News that nearly all of the thousands of newly examined emails on Weiner's laptop were duplicates of emails already seen by the team investigating Clinton's server. [...] There were unseen emails, the official said, but they were unrelated to government business. The new letter indicates that the FBI's review is completed. Neither Comey nor the FBI are expected to release any other statements.

FAQ:

What are these new emails?

Good question!

In an unrelated case, specifically an investigation into Mr. Weiner, some of the emails found on a laptop belonging to Mr. Weiner are thought to possibly have some relevance to their completed investigation into Hillary's use of a personal email server. However at this point, it has not been made clear what these emails would be, or why they would be on this person's laptop.

But that's about where the current news ends. The FBI has not yet even reviewed these emails to know if there are even new emails they have not previously reviewed. For reference: New York Times article, referencing a letter by the FBI

So it seems the real question is:

Why are they making an announcement that they might have new information to investigate?

Also a very good question, one asked by many in politics, both Democrats and Republicans. It seems that FBI Director James Comey decided to send a letter to Congress to notify them that they may have access to new information without knowing what it is, against the advice of Senior Justice Department officials.

At this point it should be noted that the FBI does not normally make announcements on ongoing investigations, and many have criticized him for breaking this precedent in this case. It is still unclear if he intended to meddle in the election or not, or if he has further intentions.

So has the investigation been reopened?

No

Though there are certainly those trying to spin it to seem like it has, the investigation into the use of a personal email server in respect to classified information has not been reopened, and unless there is significant new evidence found, there's no reason to expect it will be.

So why is this unsubstantiated find in the media?

Not surprisingly, the Republican presidential campaign has jumped at this tidbit the FBI has dropped. The subject of the email server has been a recurring topic throughout the campaign, despite the conclusions of the justice system. This unsubstantiated bit of information is being used to try to validate what has essentially been dead horse beating, again with no knowledge as to what is even contained in these emails.

So what was the big deal with the emails before? Why was she being investigated?

She was being investigated for possible violations of the storage of classified information.

Our investigation looked at whether there is evidence classified information was improperly stored or transmitted on that personal system, in violation of a federal statute making it a felony to mishandle classified information either intentionally or in a grossly negligent way, or a second statute making it a misdemeanor to knowingly remove classified information from appropriate systems or storage facilities. -- FBI Press Release

Note that they are not investigating if classified information was stored, just if it was mishandled intentionally, or in a grossly negligent way. In this case, intent and gross negligence is relevant, and one of these must be proven for there to be a case here.

Now if either of these could be proven, this would be a serious issue, and and thus this investigation was worthy of being a "big deal", but again this investigation concluded that neither of these were the case.

For reference:

Title 18, Section 793, (f):

(f) Whoever, being entrusted with or having lawful possession or control of any document, writing, [...] or information, relating to the national defense, (1) through gross negligence permits the same to be removed from its proper place of custody or delivered to anyone in violation of his trust, or to be lost, stolen, abstracted, or destroyed, or (2) having knowledge that the same has been illegally removed from its proper place of custody or delivered to anyone in violation of its trust, or lost, or stolen, abstracted, or destroyed, and fails to make prompt report of such loss, theft, abstraction, or destruction to his superior officer— [...]

Title 18, Section 2071

(a) Whoever willfully and unlawfully conceals, removes, mutilates, obliterates, or destroys, or attempts to do so, or, with intent to do so takes and carries away any record, [...], document, or other thing, filed or deposited with any clerk or officer of any court of the United States, or in any public office, or with any judicial or public officer of the United States, shall be fined under this title or imprisoned not more than three years, or both. (b) Whoever, having the custody of any such record, proceeding, map, book, document, paper, or other thing, willfully and unlawfully conceals, removes, mutilates, obliterates, falsifies, or destroys the same, shall be fined under this title or imprisoned not more than three years, or both; and shall forfeit his office and be disqualified from holding any office under the United States. [...]

(Abbreviated and emphasis added.)

But why use a personal email server if not for some nefarious purpose?

There is actually a well-documented technical problem for which the personal email account was setup to solve, and it's actually kind-of a sad issue. The government-issue BlackBerry device can only use one email account (yes, the all but forgotten BlackBerry, which many would no longer consider a maker of smart devices). I think most of us would agree it's unreasonable to have access to just your work email throughout the day (I certainly get mission-critical email in my personal email), and the only other alternative would be to carry two whole devices to work around this issue.

You can argue all you want about how she should have just used 2 devices or whatever, and in hind-sight she openly agrees that she should have, but this is not the issue the FBI was investigating so let us not get side-tracked.

Also, remember not to assume malice when intentions are unknown. This certainly fails the philosophical principal of Hanlon's razor:

Never attribute to malice that which is adequately explained by stupidity.

or

Don't assume bad intentions over neglect and misunderstanding.

Personally, I think any "smart device" which can't handle multiple email accounts is actually a pretty stupid device.

Just think, if we must start assuming malice when intentions are unknown, we must also assume that Mr. Comey sent this letter simply to meddle in the election, and this whole thing falls apart very quickly.

But I desperately want her to be guilty of something!

That's not a question, but if the voting on the hopefully highly-factual answer is any indication, this is quite-possibly true for some for you (if not, please post a comment or suggest an edit, this question desperately needs a solid answer without the speculative and slanderous baggage found above). But remember, it is not your place to decide if she is guilty or not, the justice system has already made their decision, inline with what the FBI investigation concluded.