Sputnik was the first rocket to go into space, launched in 1957. It transmitted a radio bleep. Three months later it burned up. Later that same year, Laika the dog was the first living creature to go into space. The dog was fitted w/ a special suit, but perished in space. Sputnik essentially started the "space race".
As you may have seen on "Who Wants to Be a Millionnaire", Sputnik is Russian for "Traveling Companion". The base of the monument houses the Cosmonaut Museum. The avenue in front of the monument, leading to Prospekt Mira, is lined w/ sculptures to the "heroes of the cosmos".