Gaara's powers originated due to his association as the host of Shukaku, the One Tailed Beast, a construct of mythic power composed of living chakra. Shukaku's power was the ability to control sand and transfers this gift to its host to help protect it against threats.
Chosen from birth as the jinchūriki, Gaara of the Sand Waterfall, had a large amount of stamina and huge levels of chakra and thus is able to use many chakra-taxing sand-based techniques, sometimes in quick succession, before becoming exhausted.
As a trained shinobi, he learned how Shukaku's powers worked, augmented and adapted them to a technique he would retain even after Shukaku had been removed from him. Gaara could manipulate any sand but it was easiest if he was manipulated sand that was already infused with chakra. He carried a gourd on his back of chakra-infused sand with him to make it easier for him to perform his techniques.
In some ways he became even more powerful since so much of his chakra had been tied up in controlling the jinchūriki. Without it he was able to increase the amount of sand he could control as well as interact with spiritual powers which augmented his defensive powers.
The forth Kazekage theorized that Gaara's mother was the source of his Sand Shield technique as she died in childbirth and is believed to have linked her soul to his.