Eclipse is an IDE for developing/debugging any one of several languages (usually Java - I assume that is your language of interest).
Apach ant[
^] is actually an acronym for "Another Neat Tool" but is really a compile environment; generally an xml based replacement for the makefile system.
Apache Tomcat[
^]is an Apache web server.
Eclipse and ant run on most platforms. Tomcat is unix/linux only.
[rev.1: Tomcat is a web server not a browser.]