Hi, yes, single mother is a common phrase. Also single mum.
It means a mother who raises her family with no resident father. She could be a widow, she could be divorced or separated, she may have lived with the father in the past but no longer, she may never have lived with the father. She is 'single' in the sense of not having a partner, and a mother.
I really don't know how to thank you , nona, all I can say is that you're most welcome in my house when ya come to K.S.A. THANKS from within my heart...