A Program Executive Office (PEO) is the main stakeholder responsible for the cost, schedule, and performance in a DoD acquisition program and/or portfolio. A PEO may be responsible for a specific program (e.g., the Joint Strike Fighter), or for an entire portfolio of similar programs. 
Definition: The Program Executive Officer (PEO) is the individual responsible for all aspects of a specific program, or a portfolio of similar acquisition programs in the Department of Defense. Basically the big boss.
Program Executive Office (PEO) Assignments: 
- Unless a waiver is granted for a particular program by the Under Secretary of Defense (USD) Acquisition, & Sustainment (A&S), Component Acquisition Executives (CAEs) shall assign acquisition program responsibilities to a PEO for all Acquisition Category (ACAT) I, IA, and sensitive classified programs, or for any other program determined by the CAE to require dedicated executive management.
- Unless a waiver is granted by the Defense Acquisition Executive (DAE) or CAE, a PEO shall be experienced and certified in acquisition management. Waivers should be strictly avoided. The PEO shall be dedicated to executive management and shall not have other command responsibilities unless waived by the USD (A&S).
- The CAE shall make this assignment no later than program initiation or within 3 months of estimated total program cost reaching the appropriate dollar threshold for ACAT I and ACAT IA programs. CAEs may determine that a specific Program Manager (PM) shall report directly, without being assigned to a PEO, whenever such direct reporting is appropriate. The CAE shall notify the USD(A&S) of the decision to have a PM report directly to the CAE.
- Acquisition program responsibilities for programs not assigned to a PEO or a direct-reporting PM shall be assigned to a commander of a system, logistics, or materiel command. In order to transition from a PEO to a commander of systems, logistics, or materiel command, a program or increment of capability shall, at a minimum, have passed Initial Operational Capability (IOC), have achieved full-rate production, be certified as interoperable within the intended operational environment, and be supportable as planned.
In the Air Force, Air Force Instruction (AFI) 63-101 provides responsibilities for both the Program Manager (PM) and the PEO in Chapter 3, Subpart 3.14 and 3.16. 
AcqLinks and References:
-  DoD Instruction 5000.02 “Operation of the Defense Acquisition System” Enclosure 10
-  Website: Wikipedia – Program Executive Officer
-  Website: ACQuipedia – Program Executive Officer