The cap has multiple purposes.
One purpose is to "filter" voltage ripple and other unwanted signals coming in from the power source.
A second purpose is to provide a buffer of current capability for brief periods when your device wants a lot of current.
A third purpose is to prevent brief periods of high current demand from your device, from lowering the voltage of the power source and potentially affecting other devices using that source.
These purposes are all inter-related but their conceptual importance depends on the context. It would be unwise to get the concept stuck in your head that these are "filter" capacitors, and that that is the only relevant purpose.