The a minore ad maius argument denotes an inference from smaller to bigger.
A notable example is contained in Tractate Ketubot on page 44b. R. Jose b. Hanina rules that a man who brings an evil name upon an orphan girl is exempt since the Bible states in Deut. 22:29 "And give them unto the father of the damsel," which excludes a girl who has no father. R. Jose b. Abin (some attribute this to R. Jose b. Zebida) objects and quotes R. Jose the Galilean that we learn from "If the father shall utterly refuse" (Ex. 22:16) that an orphan is, in fact, included in the fine. This said, how can she be included here and excluded there [in that of an evil name]?! He answers that this [ruling of R. Jose the Galilean] is a case of an orphan girl who became an orphan after the man had intercourse with her [and the ruling of R. Jose b. Hanina still stands]. Rabbah argues on this and states that the man who brings an evil name upon an orphan is obligated to pay the fine nonetheless for Ammi taught "A virgin of Israel (Deut. 22:19) and not a proselyte virgin" i.e. the penalties spoken of in the Scriptural text apply only to the former and not to the latter. If you assume that in a case of a proselyte in Israel [who is not considered to have parents and is, thus, considered an orphan] guilt is incurred, one can well see why it is necessary for a Scriptural text to exclude proselytes [i.e. R. Jose b. Hanina's ruling from Deut. 22:29]. If, however, you assume that in the case of an Israelite girl who is fatherless the offender is exempt, a difficulty would arise. If the offender would be exempt even against Israelites, would it have been necessary to mention exemption if the offense was against proselytes?! [Of course not, since the latter case would be self-evident a minore ad maius. As exemption, however, was specified in this case it may be concluded that in that of an Israelite orphan guilt is incurred]. Thus, Rabbah uses the a minore ad maius to maintain his refutation of the ruling of R. Jose b. Hanina.
The reverse and more universally known argument is a maiore ad minus, which also usually has a broader usage. The meaning of the a maiore ad minus argument is incomparably more general. It pertains to applications of the a fortiori argument.