Wiktionary
n. (context Mormonism English) The responsibility of the priesthood in which a pair of priesthood holders visit another member's family to teach them LDS doctrine and see how they are doing. vb. (present participle of home teach English)
Wikipedia
Home teaching (formerly called block teaching and ward teaching) is a responsibility of priesthood holders in The Church of Jesus Christ of Latter-day Saints (LDS Church). Home teaching is a church program designed to allow families to be taught in their own homes, in addition to weekly church services. Typically, two holders of the priesthood, of whom at least one must be an adult, visit the home of some assigned families at least once a month. Home teaching is organized at the ward level.