A nice distinctive feature of the Tetons is having a big flat open area to appreciate them from.
The Tetons themselves are formed from very old Precambrian gneiss, with a few granite plutons and many diabase dikes running through them. During the Paleozoic, these rocks were overlain by many thousands of feet of sedimentary rocks. Many cycles of deposition and erosion followed, but the next really interesting event (aside from the huge Yellowstone eruptions) was the emergence of the Teton fault about 9 million years ago.
The Teton fault runs north-south along the eastern foot of the currently-existing mountains. Rocks west of the fault pushed upwards, rocks east of the fault simultaneously dropped downwards. Volcanic ash, glacial deposits, and river sediment filled in the cavity that resulted from the downfaulting of the valley floor, filling it to the current depth and leaving it generally flat. The thousands of feet of sedimentary rock covering the rising mountains eroded away completely, except for a small cap of sandstone on Mt. Moran (the flattish peak to the right). The equivalent layer of sandstone is about 24,000 feet below the surface of Jackson Hole, implying a total movement along the fault of about 30,000 feet, at an average rate of displacement of 4 inches per hundred years.
The sediments of the valley floor tend to drain water very quickly, so relatively little water is available for surface plants. This results in grassy, generally open plains, with trees mostly occurring on the denser soils of old glacial moraines. (Or so I've read.)