This item is a charming and unique pair of Tibetan cushion-cover rugs (gyabney), pile rugs that covered stuffed cushions used as backrests, probably in a monastery. Based on the dimensions, another, perhaps less likely, possibility is that these rugs are shugden, small sitting rugs used for honored guests. For these functional types, see generally Trinley Chodrak and Kesang G. Tashi, Of Wool and Loom: The Tradition of Tibetan Rugs (Trumbull, Conn.: Weatherhill, 2000), at pages 101 and 141.
All of the motifs on these two rugs relate to the theme of long life. The central figure is Shou Lao, the god of longevity, who is here shown wearing Tibetan-style nomadic boots. To the left of Shou Lao is the Chinese character or ideogram for long life; to the right of Shou Lao is a crane, another symbol of longevity.