Whenever Chiyo [his grandmother] sealed Shukaku into his body [because of his dad burning_eyes ]
Since Shukaku's a demon he pretty much made Gaara own everyone else... How far have you watched/read [which ever you do] so I know not to ruin something else... [something after the time skip when Gaara owns everyone a lot more]
Sorry for correcting you but Chiyo is not Gaara's Grandmother, she is Sasori's.sweatdrop Gaaras' power stems from the Shukaku but somehow it also comes from the love of his deceased mother.