Need help with broken plastic pipe in the yard, constant stream of water
I'm assuming this pipe connects your gutters to the cities storm drain system, depending on the type of pipe and the damage it's probably a simple fix.
If the pipe is PVC and the damaged area is not too large, you may be able to cut out the damaged section and reconnect it using a coupling.

If the damaged area is larger (and PVC) you could cut out the damaged area, then patch it in using another length of PVC and two couplings.
If the pipe is not PVC you could use a flexible rubber coupling as @AWMoore suggests, just make sure the one you use is rated to be buried (and is permitted to be buried by your local codes).

If this is a storm drain you may want to contact your local water municipality, as they may be responsible for the maintenance of the drain line (paid for by your taxes).