What does it mean to marry in mass?

Assuming you mean "en masse", it is when a large group of couples marry in the same ceremony. Cult leader Sun Myung Moon is well-known for performing such ceremonies. These ceremonies are called blessing ceremonies or "mass weddings".

In Roman Catholicism, Marriage is a Sacrament , solemnized by a ceremony in Church with a special Mass or Celebration of the Holy Eucharist. Not " en masse " , as in a group.

Roman Catholic AnswerTo marry in Mass is to have the marriage ceremony performed during the celebration of the Eucharist after the homily, it is called a Nuptial Mass.

from Modern Catholic Dictionary by John A. Hardon, S.J. Doubleday & Co., Inc. Garden City, NY 1980

Nuptial Mass The Mass at which a Catholic is married. With a bishop's permission, a nuptial Mass may be offered in a mixed marriage when the non-Catholic partner is baptized. The ritual provides for the marriage to be performed after the Gospel and homily, with the nuptial blessing after the Lord's Prayer, and a special blessing of bride and groom at the end of the Mass.