There are a few meanings. If you haven't heard it before, I am guessing you hear it in a context like "the LAMP stack." Basically, web applications are complex systems these days, and they rely on moving parts on top of moving parts. Stack describes that collection of programs/technologies.
For example, Bingo Card Creator uses a fairly typical Rails stack: application code in Rails(a web framework based on the language Ruby), MySQL for the DB, Nginx proxying to mongrel for the web tier, memcached and Redis for for a few purposes, DelayedJob for queuing, all running on Ubuntu.