When i send BTC i have to pay a transaction Fee who gets it and Why?
The solo-miner (or mining pool) that confirms your transaction into the blockchain gets to claim the transaction fee for providing you this service.
Another perfect answer from DM.
In the design, bitcoin block reward will be halved every 210000 blocks (about 4 years), and will be zero (in about 2140).
So, the tx fee will be more and more important, and eventually it will be the only incentive to get people mining bitcoin blocks.