Whatever the Attorney General Jeff Sessions tells him to investigate.

Robert Mueller, Special Prosecutor, is pictured above on the left. The man in the U.S. Secret Service hockey jersey is unidentified.

The source is Federal Code § 600.4, "Jurisdiction of a Special Prosecutor":

(a) Original jurisdiction. The jurisdiction of a Special Counsel shall be established by the Attorney General. The Special Counsel will be provided with a specific factual statement of the matter to be investigated. The jurisdiction of a Special Counsel shall also include the authority to investigate and prosecute federal crimes committed in the course of, and with intent to interfere with, the Special Counsel's investigation, such as perjury, obstruction of justice, destruction of evidence, and intimidation of witnesses; and to conduct appeals arising out of the matter being investigated and/or prosecuted.

(b) Additional jurisdiction. If in the course of his or her investigation the Special Counsel concludes that additional jurisdiction beyond that specified in his or her original jurisdiction is necessary in order to fully investigate and resolve the matters assigned, or to investigate new matters that come to light in the course of his or her investigation, he or she shall consult with the Attorney General, who will determine whether to include the additional matters within the Special Counsel's jurisdiction or assign them elsewhere.

(c) Civil and administrative jurisdiction. If in the course of his or her investigation the Special Counsel determines that administrative remedies, civil sanctions or other governmental action outside the criminal justice system might be appropriate, he or she shall consult with the Attorney General with respect to the appropriate component to take any necessary action. A Special Counsel shall not have civil or administrative authority unless specifically granted such jurisdiction by the Attorney General

http://judicial-discipline-reform.org/docs/28cfr600_Independent%20_Counsel.pdf