West Germany (German: Westdeutschland) is the common English name for the Federal Republic of Germany or FRG (German: Bundesrepublik Deutschland or BRD) in the period between its creation in May 1949 to German reunification on 3 October 1990.
During this period, the NATO-aligned West Germany and the socialist East Germany were divided by the Inner German border. After 1961, West Berlin was physically separated from East Berlin as well as from East Germany by the Berlin Wall. This situation ended when East Germany was dissolved and its five states joined the ten states of the Federal Republic of Germany along with the reunified city-state of Berlin. The enlarged Federal Republic of Germany with sixteen states (known simply as "Germany") is thus the continuation of the pre-1990 Federal Republic of Germany.
For more detailed information and history see Wikipedia:West Germany