what is this?

LAst5.0 has it exactly right. It's part of the emissions system. Basically, liquid gas doesn't burn - but the vapors do. Older cars just vented the vapors to open air, but our Stangs have a system to reclaim and burn them. The vapors are collected in a charcoal canister in the passenger fender, and at partial throttle (I believe) the canister purge solenoid (CANP) opens up. Engine vacuum draws the vapors from the charcoal canister into the intake to burn them. If either of the hoses from the intake to the CANP or from the CANP to the charcoal canister are cracked, you can get a gasoline smell seep through the vents and into the passenger compartment.

TL;DR - the CANP doesn't affect power in any way, and it doesn't weigh much. I personally would replace the hoses, hook it all back up and let it do its job. Up to you.