The gambit is named after Captain William Davies Evans, the first player to employ it. The first game with the opening is considered to be Evans - McDonnell, London 1827, although in that game a slightly different move order was tried (1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. O-O d6 and only now 5. b4). The gambit became very popular shortly after that, being employed a number of times in the series of games between McDonnell and Louis de la Bourdonnais in 1834. Players such as Adolf Anderssen, Paul Morphy and Mikhail Chigorin. It was out for favour for much of the 20th century, although John Nunn and Jan Timman played some games with it in the late 1970s and early 1980s, and in the 1990s Garry Kasparov used it in a few of his games (notably a famous 25-move win against Viswanathan Anand in Riga, 1995), which prompted a brief revivial of interest in it.
The basic idea behind the move 4. b4 is to give up a pawn in order to secure a strong centre and bear down on Black's weak-point, f7. Often, the idea of Ba3, preventing black from castling, is also in the air. The most obvious and most usual way for black to meet the gambit is to accept it with 4... Bxb4, after which white plays 5. c3 and black usually follows up with 5... Ba5 (5... Be7 and, less often 5... Bc5 and 5... Bd6 are also played). White usually follows up with 6. d4.
Alternatively the gambit can be declined with 4... Bb6, when 5. a4 a6 is the normal continuation.