Buraimi is the Omani half of the Al Ain oasis, which straddles the border between Oman and the UAE. Most of the major sights — the forts, the oasis gardens, the camel market — are on the UAE side in Al Ain proper, but since the border crossing here is straightforward, this is not much of a limitation.
The practical reason to stay in Buraimi rather than Al Ain is price: hotels on the Omani side are significantly cheaper. Most Omani shops accept UAE dirhams, though the reverse is not always true. The Omani side has its own attractions — the Al-Khandaq Fort, a working camel souq, and the dramatic mass of Jebel Hafeet rising on the southern horizon.
Note that UAE taxis cruise around on the Omani side but refuse to use their meters while in Oman. Negotiate a fare in advance, or walk to the border roundabout if your hotel is nearby.