To be admitted means to be accepted or allowed into a group or organization. In the context of Bleeding Kansas, it refers to the process by which a territory could become a state and join the United States.
Related terms
Statehood: The status of being an independent political entity within a larger country, in this case, joining the United States as a new state.
Territory: A region that has not yet achieved statehood but is under the jurisdiction of a larger governing body, such as Kansas before it became a state.
Congressional Approval: The process by which Congress reviews and decides whether or not to admit a territory as a new state.