Purusha is the Gita's word for the conscious person within: the one who experiences, as distinct from prakriti, nature, which acts. The distinction is old and practical. It helps explain why we can watch our own thoughts, why we are not identical to our moods and why a person can feel unstained by events even in hard times. It gives a name to the quiet presence behind experience.
Gita 13.21 says bodily and mental activity is produced by nature, while the conscious self is the experiencer of pleasure and pain through identification with that activity, so notice how identification with outcomes creates your joy and sorrow. Gita 5.14 says that actions, doership and their results arise from prakriti while the Self remains a detached witness, and Gita 13.32 says the Supreme Self does not act and is untouched by the results of what the body does.
The Gita also names two kinds of purusha. Gita 15.16 says that in the world there is the perishable, which includes all created bodies and things, and the imperishable, which is the changeless principle within existence, so distinguish what changes from what endures and invest less in passing circumstances. When troubled by guilt, shame or turmoil, recall that your deepest self is unstained by the passing events of body and mind, while still taking responsibility for what you can repair.