This line comes from Kate's eloquent speech at the end of Act 5 in Taming in the Shrew. Kate is admonishing the widow and Bianca to place their hands under the feet of their husbands in a gesture of servitude.
The image evoked here is that of foot washing that appears in the New Testament in which Jesus humbled himself to wash the feet of his disciples. In the bible verse (John 13), Jesus is showing that serving is a noble act.
Foot washing or placing one's hands below the foot of another was traditionally done by a servant to a master, a wife to a husband, a disciple to a mentor. But it was not viewed as an act of humiliation, but rather an act of respect and honor. In this way, Kate is showing that wives (or husbands for that matter) should not be too proud to serve their spouses or to try to make their lives easier, more peaceful, and more harmonious.