A catechism takes the form of a series of questions and answers to be memorised and repeated, and is used to inculcate Christian beliefs in children and converts particularly. The Reformation ushered in a spate of these, but it was the Westminster version that was to become the central guide of the Presbyterian Church of Scotland. This combined Calvinist teachings with a pragmatic emphasis on the moral law enshrined in the Ten Commandments. Rev. Wringhim is reading from the shorter version. Hogg is undoubtedly thinking of his own childhood here, for repeating the shorter catechism was a ritual he and has father performed each Sunday and which he would go on to perform with his own children.
The Westminster Shorter Catechism can be read here.