In plain words
A short book of the basics of the faith. Luther wrote one for families.
The fuller definition
A short handbook of the basics of the faith, usually in questions and answers, meant to be learned and talked over. Lutherans mean above all Luther’s Small Catechism of 1529, written for families to use at home, and his Large Catechism for pastors and adults.
In Lutheran writings: The creeds, the catechisms, and the other documents in the Book of Concord.