I disagree with the negative takes on this. When I hear, "Fast-paced environment", I think "lots of interesting responsibilities, because work gets done effectively so you can move on to something else". I would describe my current work environment as "fast-paced", but I would also rave about the work-life balance I get.

I think the issue is that recruiters confuse "fast-paced" with "we have lots of emergencies and make people put in lots of hours" - which is almost the opposite of fast-paced. Emergencies derail and randomize people, slowing down the pace of business. Working long hours is a symptom of not being fast-paced during normal business hours, and trying to make up for it by working more. "Working hard, long hours while being randomized when things go wrong" and "producing great business value rapidly" are two different, often contradictory things.

"Fast-paced", in the sense of "our team delivers lots of business value in a short period of time," is desirable because it leads to an improved work-life balance. You get great resume content and develop your talent without investing lots of time into independent study in your own time, since you are learning so much on the job - meaning your free time can be spent on non-programming hobbies without your skills becoming obsolete. "Fast-paced" is also not boring, since you complete one project quickly and then can move on to something fresh. IMO, constantly dealing with emergencies and "fires", covering for other people's mistakes, coping with crummy tools and poor documentation, and so on, is very frustrating and boring.

Edit: I thought of a few other things "fast-paced" implies that are positive and can be attractive: First, it suggests that the team uses Agile practices; waterfall isn't fast-paced. Second, it implies that the company or team is small and light-weight, and not bound up in miscellaneous process; people who sit in lots of meetings and need to fill out three forms for each bug fix aren't going to be moving quickly. Third, it hints at a growing company (maybe a start-up?) or team that is making strides and delivering lots of value to their customers, vs. a company or team that has already done its interesting work and is now just sitting there doing maintenance and getting money for the work they already did.

One comment below also points out that "fast-paced" is a contrast to "in-depth". A fast-paced environment is one where you pick up a lot of skills in a very short time, but may not become an expert in any of them. A slower environment where lots of experts are needed and things need to be done well the first time is more likely to grow in-depth skills. Having lots of breadth in one's skills and having a few skills in depth are very different career tracks, so "fast-paced" is also a signal that people who want to become experts at a relatively narrow set of skills probably shouldn't apply.