BABYLON 5, I thought, had a good take on what it means to be a telepath, explained pretty well by Byron, actually.
Garibaldi once was coming toward Byron, and he immediately told Garibaldi 'no'. He was obviously confused at the moment because he didn't ask Byron anything yet, but Byron let him know he could hear his thoughts from all the way across the deck. Byron wasn't even trying to scan him... his thoughts were simply loud.
Byron then went on to explain that it takes constant distractions to just avoid picking up thoughts every second... singing songs, doing nursery rhymes, etc. It painted being a telepath as being extremely exhausting just to live.
Tam Elbrun is a good ST equivalent.