In essence know what goes on when you do something. It runs the specified ASP file as is at the point you call it. Once the file has been completely executed, control comes back to the calling page. The advantage is that the called file is only cached once, even if multiple pages call it. A drawback of the Server.
Execute method is that the script that is called is cached on it's own.
So like with includes, this should be used wisely. In some cases Server. Execute and include are interchangeable. You can then test both cases under load and see which performs better. Another drawback of the Server.