Just to provide a little more information about the use of netstat. The command line option -p (as suggested above) will cause netstat to display the program that is associated with the socket/port. In this case exim should show up in the output indicating that is is responsible for the port 25 connection. But, there is a slightly subtle detail about the use of this option. Due to security netstat will only show you program names for applications you own. So if your not already doing your testing as root netstat will not show you what application owns port 25. In general one should not get into the habit of running around as root, but in this case it is a helpful step.
Another detail somewhat related here is the use of telnet. This application is an often missed network analysis tool. A very fast test to see if port 25 is doing anything is to just telnet into it (this works great for any number of other service ports). Try telneting to localhost, 127.0.0.1, your IP and your hostname. The reason I point this out is that exim might well be runing and might well have opened port 25 in some fashion, but if something is broken about exim (say somebody messed with the config file in an ungraceful way) the use of netstat will not tell you port 25 is not talking. And, a quick telnet in will.
If you want to feel unixy old school you can use nc for the same purpose. Or, if you prefer the sledge hammer approach look at the man page for nmap (I actually do not recommend looking at this man page for a newer user though, nmap is hideously complicated). And for more fun, try telneting into the ssh port, it's instructive.