What size wire needed for 100a subpanel 120ft away from house sub panel? Biggest amp draw will be a window A/C unit, and a pool pump
You want 3 1AWG Al XHHW-2s here with an 8AWG ground

Since we are running a feeder here (and a 100A one at that), we can use the 75&deg;C column in the ampacity tables, which gives us a 1AWG aluminum wire for 100A.  However, SER cable is the wrong type of thing to use here; instead, we want individual 1AWG aluminum wires, preferably with XHHW-2 insulation as that withstands the rigors of outdoor use the best; with this, we can use an 8AWG copper ground wire, either bare or THHN insulated, your pick.

Go big or go home!

You will want a 100 or 125A, 24 or 30 space (note I said space, not "circuit", as double-stuff breakers aren't nearly as useful as they seem), main breaker panel at the shed, or a larger one if you can get it, for that matter.  It is not an issue if the panel's main breaker is larger than the feeder breaker in the main panel, by the way, as all the main breaker is in this case is a convenient way to get a shutoff switch at the shed.

TORQUE ALL LUGS TO SPEC

One other thing you will need to do with this installation is use an inch-pound torque wrench to torque all loadcenter and circuit breaker lugs in what you are installing to their marked tightening torques.  This is required by 110.14(D) in the 2017 NEC, and is a good idea anyway even if your AHJ has not adopted the 2017 edition of the Code yet, lest your electrical system get a case of the loose lugnuts!