Function of the Auricle in heart
The left auricle is a decompression chamber when atrial blood pressure is high (in systole or in some pathological conditions) [1, 2]. Some research claims it also plays a role in cardiac regeneration because it contains cardiac progenitor cells [3].

Probably the right auricle has less important function; also there are fewer studies about it.



References:


Al-Saady NM, Obel OA, Camm AJ. Left atrial appendage: structure, function, and role in thromboembolism. Heart. 1999 Nov;82(5):547-54. PubMed PMID: 10525506. 
Bansal M, Kasliwal RR. Echocardiography for left atrial appendage structure and function. Indian Heart J. 2012 Jul 27;64(5):469-75. doi: 10.1016/j.ihj.2012.07.020. PubMed PMID: 23102384. 
Leinonen JV, Emanuelov AK, Platt Y, Helman Y, Feinberg Y, Lotan C, Beeri R. Left atrial appendages from adult hearts contain a reservoir of diverse cardiac progenitor cells. PLoS ONE. 2013 Mar 12;8(3):e59228. doi: 10.1371/journal.pone.0059228. PubMed PMID: 23555001.