Generally, HTTP and FTP protocols in Internet use the client-server architecture. Here the client computer will just connect to the server computer. One client will not connect to another client. When many clients connect to the server the speed of the server will slow down. Both installation and usage of client-server is very easy.
Peer-to-peer method was introduced as an alternative to Client-server architecture. Grutella, eDonkey, Kazaa etc used peer-to-peer architecture. Whoever is connected to the network can send or receive files from any computer in the network. When a computer sends some files to another computer it functions as a server and when it receives a file from another computer it functions as a client.
Since a file can be shared between any file and not shared from a central server there is no way to track which files are being transferred. Therefore many started sharing illegal audio and video files using these peer-to-peer software. Peer to Peer software enables speedy transfer of files.
Bit Torrent method uses the best features of Peer-to-Peer and Client-server architectures. Computers get the different parts of a file from the 'seed' and then the computers share these parts of the file from other computers and completes the file.