What is happening in this part of the LC3?
This would appear to be a picture of the LC-3 data path from the book Patt, Yale N; Patel, Sanjay J: Introduction to Computing Systems.

The IR is the instruction register, the register where the actual bits of the instruction are fetched in the beginning cycles of processing the instruction.  The SEXT unit takes the immediate field out of the instruction.  The SR2MUX is used by the control unit to control whether the second operand of the instruction comes from a register operand or the immediate operand.