Look the Higgs is a postulated particle. It was born as a mathematical trick in order to solve some problems concerning symmetry in quantum field theory. The Higgs has mass because we defined it like that. The Higgs particle gives mass to elementary particles via it's interaction with these particles. This interaction can be expressed in terms of a coupling between the higgs field and the elementary particle field. The coefficient of the product of these fields is the mass of the elementary particle. This is just how the QFT formalism works. This is all very nice but the question remains as to wether this is true. This is why many scientists await the first experimental verification of this system of spontaneous breakdown and mass generation. Also, elementary particles need to be massless when in gauge theory because of symmetry reasons. I have written many topics on this in my journal, go check it out
search for the entries on the Higgs field and 'why elementary particles are massless'
This is very interesting stuff but not that easy.
Also i read analogy stuff like 'the gravitons are the photons'. Do not pay any attention to this because it is fundamentally wrong. Gravitons are very different in nature, they indeed mediate the gravitational force but they are different in nature because they ARE particles of space time itself. There is not such a think as gravitational radiation or some sort. If this were the case, the analogy with photons is justified. Keep this in mind...
Scroll down to the Higgs field entry and read why elementary particles are massless on the next page (8)