Ant is a java based build tool, kind of like Make or GnuMake, iMake etc. The difference is that instead of shell scripts the build process is 'scripted' in xml files which are then processed by ant.
These xml files call out to java classes to perform the specified function. Being java based makes your build platform independent and you can also write your own tasks to supplement or extend those provided by Ant.
For mor info check out: http://jakarta.apache.org/ant/
I am not very familiar with Velocity but I believe it is a template engine which allows for easier development of web pages. I believe it allows the web designers to make the pages more dynamic by including calls to java code without really having to deal with the code. You can find more aobut it at: http://jakarta.apache.org/velocity/user-guide.html#What%20is%20Velocity?