What role does potassium iodide play in the generation of oxygen?

Are you referring to the "Elephant Toothpaste" reaction, in which KI is added to hydrogen peroxide?

In this reaction the KI (more exactly, the iodide ion) acts as a catalyst.

The reaction takes place in two steps.

Step1: H₂O₂ + KI → H₂O + KOI

Step 2: H₂O₂ + KOI → H₂O + O₂ + KI

Note that the KI reacts in the first step but is regenerated in the second step. The KI can be recovered unchanged at the end of the reaction, so it is a catalyst.