In simple terms (the way I'm managing to understand it) is that it's better to think of it as a field that adds mass to things. It's like a tray of stick stuff -- say treacle -- that stops other particles rolling around so much. The heavier the particle, the more effect it has on them. Because a heavier thing would sink into the treacle more and so would feel heavier if you tried to move it.
Another way I've heard it described is to think of someone walking through a crowded room. They could reach the other side relatively undisturbed. If someone famous tried it (having more 'weight') they'd attract more people as they went (Higgs) and be slowed down and hampered.
So in essence it seems to stop other particles flying around like crazy fools.