What are TH2 keys and DOTA2 Keys exactly and what are they worth?

They're in-game items. Their primary purpose is opening crates/treasure boxes for mystery loot, but they're often used as currency in trades.

As far as what they're worth, it depends on what context you're talking about. They're $2.50 if purchased directly from the TF2/DOTA2 store, anywhere from like $2.20-$2.40ish if purchased from the market (which works out to about $2 worth of Steam wallet to the seller after Steam takes their cut), or like $1.35 if you find someone selling them for paypal and you're willing to take that risk.