From https://wiki.mozilla.org/Performance/MemShrink:
"MemShrink is a project that aims to reduce Firefox's memory consumption. There are three potential benefits.
1. Speed. Firefox will be faster due to less cache pressure, less paging, and fewer/smaller GC and CC pauses. Changes that reduce memory consumption but make Firefox slower are not desirable.
2. Stability. Firefox will suffer fewer aborts/crashes due to virtual or physical memory exhaustion. The former is mostly a problem on 32-bit Windows builds with a 2GB or 4GB virtual memory limit, the latter is mostly a problem on mobile devices that lack swap space.
3. Reputation. Fewer people will complain that Firefox is a memory hog and that Mozilla ignores memory usage."
MemShrink has been running since June 2011 and there have been many improvements in Firefox's memory consumption since then; these have shown up in Firefox 7, 8, 9, 10 and 11.
Edit: The sentence above is sarcastic. Firefox has had better memory usage than its competitors for a while now, despite the belief that it is leaky.