A mass intention is a specific request for which the Mass is offered. Mass intentions are most commonly offered in remembrance of a person who has died. However they can requested on behalf of another living person such as for healing and commemorating a wedding anniversary.
When a priest celebrates Mass, he offers each celebration of the Eucharist for a particular person, or intention. By doing so he applies special graces from God upon that person or intention. The Church is able to intercede for us through the celebration of the Mass that possess a power greater that our personal prayers.