Interfaces help to clarify the distinction between different functional units. One unit depends on another unit to do something, not to be something. As long as that other can do what's stipulated in the interface (think contract), then it can be anything behind the scenes.
For example, I have a entry processor that reads entries from one place, and writes them to another place. It doesn't care from what/where, or to what/where. All it cares is that it's getting the entry from some type of reader (using the IReader interface) on once side, and handing them off to some type of writer (using the IWriter interface).
In my first implementation, the IReader implementer gets stuff from a SQL database, and the IWriter implementer posts it via a web service client. However, we'll eventually create other implementers on either end to access other repositories (FTP sites, directories of files on a local network drive, etc.).
All this time the processor in the middle doesn't care and doesn't change. It just talks through those standard interfaces.
Theoretically you could use a base class (preferably an abstract one) instead of an interface, but that's starts to lock your modules more tightly together, which makes your system harder to maintain. Lose coupling really does make your life easier, even if you aren't on a team of programmers. Consider yourself as a different programmer, every time you work on a different part of your system. Each time you revisit a given section, you have to relearn what it does to maintain it. If every piece of your system is tightly coupled with every other piece, then you must have a constant, intimate knowledge of the entire system, not just the one piece on which you're working.
There's also the concept of a single class implementing multiple interfaces, which is almost like multiple inheritance. In this situation a single class can perform multiple jobs (which can be argued is not very wise, but at least it's possible). If you chose to use a base class instead of an interface above, then this would not be possible.