Beso is correct but perhaps I can put some flesh on the bones.
In modern field theory we dont like what Einstein called "spooky action at a distance" the force is carried by particles.
The electromagnetic force by electrons, the Strong force by Gluons and we'd expect there to be gravitons.
The catch is that these are virtual when they carry force meaning we can't see them doing it.
We can however create them if we bang particles together hard enough. Thats how the W and Z particles that carriy the Weak force were found.
So the Higgs particle doesn't give things mass the Higgs field does and the particle carries the field.
So where does the Higgs particle get its mass from?
Well whereas photons don't feel the electromagnetic field, gluons do feel the strong force. They interact with each other and we think even clump together in "Glueballs"
(No I'm not kidding)
http://en.wikipedia.org/wiki/Glueball
Similarly Higgs particles would feel the Higgs field which gives them mass.
However this might still all be wrong - the Higgs might not exist. Although it's looking more like it does all the time it wouldn't amaze me if it didn't.
There are some issues with it and it would be dull if later this year they just said "yep there it is as predicted"