The name comes from a legend: a group of 75 Apache warriors were surrounded by the U.S. cavalry at the edge of a cliff in Arizona in the 1870's. They were outnumbered and rather than being killed they leapt or fell to their death. The tears of grief from the women and families of the fallen warriors solidified into the small chunks of stone we call Apache Tears.
Apache Tears are wonderful for helping you to work gently through your pain, as opposed to suppressing it. They also have some of the properties of Obsidan, protection, purification and grounding.