A closed primary is a preliminary election in which only members of a political party can vote. In the U.S., it is up to individual states and parties whether to have open or closed primaries.
Primaries determine who will run in a general election, and in a closed primary, only declared members of the Republican party can vote for a Republican candidate. Likewise, a closed Democratic primary is only open to registered Democrats. Each state has different rules about whether a primary election is open to everyone or limited to party members.