SQL "Suspends" a process when it is waiting for a non-SQL resource to complete an action. A very common example would be that a process has requested a large amount of data and the disk drives are busy processing something else. SQL will suspend a process like this until the drives respond with the requested data.
If you are seeing a lot of suspended processes, you need to use perfmon or some other tool to determine what SQL is waiting for. Check your CPU, memory, and drive usage - keep in mind that drive usage goes up if memory needs to get moved in and out of the swap file.