I believe it means that it tried to start a service, but another service that was required for this one to run, failed to start, so this one also failed.
A (bad) example is if you wanted to start an FTP server, it relies on the network running first. If the network was not already running, then, when it starts the FTP, it first would try to start the network. If the network start failed, then you would get a message like the one you got.
If you look in the system log, it should give more information about what actually failed, and then you may be able to fix it.