ASP is for Active Server Pages and is a Microsoft Based Scripting language.
JSP is Java Server Pages and is a Java Based Scripting language. JSP needs
an environment like Tomcat to process the pages where ASP is handled by IIS
(Microsoft's built in web server). ASP.NET is a newer version of ASP and
uses the .NET Framework. Check out these sites for more information.

I know this is a very high level explanation. If you have any other
questions feel free to ask.