The Bifrost Bridge (also called the Rainbow Bridge) was a bridge in Asgard used for travel between two world in the galaxy, most notably used by the Asgardians. The Bifrost Bridge was protected by its guardian Heimdall, who would also use his sword to activate the bridge.
The bridge was destroyed by Thor when his adopted brother Loki tried using the bridge to destroy Jotunheim, home of their enemies the Frost Giants. Not wishing to destroy an entire race and seeing no way to stop the bridge from using the power of Loki's staff to destroy the planet, Thor used his hammer Mjølnir to break the bridge, thus causing the outer part of the bridge to fall off.
With the Bifrost Bridge destroyed, transportation to other worlds was no longer possible for most Asgardians. Odin was able to use his magic to transport Thor to Earth, after they found out Loki had traveled there. After Thor and the Avengers captured Loki and secured the Tesseract, Thor used the Tesseract to bring him and Loki back to Asgard. This was then later used to rebuild the Bifrost Bridge.