What is the "Jazz Project" or Jazz
based projects?
I think It's a framework for component-based server-side applications, focussing on collaborative software development tools. It's hard to make out through the veil of buzzwords.
what is the role of Eclipse in Jazz based projects?
Presumably a lot of them are developed using Eclipse. You may also have heard them used together because Jazz is envisioned as a kind of "server-side Eclipse", i.e. a platform that aids development and integration of development tools.