An Overflow Pipe is so called because it is a Pipe that is fitted to a liquid container to prevent Overflow. It is positioned above a desired maximum liquid level so that, should liquid breach this height, it will be channelled through the Pipe, unable to rise any further.
In homes, Overflow Pipes are commonly fitted to the cistern, or toilet tank. Should, for any reason, the cistern begin to fill up with too much water, the water will be evacuated through the Overflow Pipe to the garden or elsewhere outside the house.
The purpose of an Overflow Pipe is therefore flood prevention. If your Overflow Pipe is releasing water this indicates that there is a problem with your plumbing that needs to be resolved.