10 Mukhi Rudraksha is the bead that was created from the tenth teardrop of Lord Shiva. There is a scenario described in the Vishnu Purana where Lord Shiva was meditating on Kailash Parvat and he was really upset with the way the humans on Earth were in pain due to a lot of miseries and issues.
These people needed some kind of help and Lord Shiva was in meditation so he could not wake up and go to help these people. Also, he knew his term on Earth was over and there was no way he could be present forever on earth to heal the miseries of everyone. So he cried over this realization.
