A more thorough explanation:

Definition: Entryman (en-tree-mən), n. Archaic. A person who enters public land and stakes a claim with the intention of settling.

An entryman is someone who goes onto public land and claims it as their own with the intention of living there. This term is not commonly used anymore, but it was used in the past when people were moving westward in the United States and settling on new land.

Example 1: In the 1800s, many entrymen traveled west to stake their claim on land that was available for settlement.

Example 2: John was an entryman who went to the government office to file his claim on a piece of land he wanted to live on.

These examples illustrate how an entryman would go to public land and claim it as their own. In the first example, it shows that many people were doing this during a specific time period. In the second example, it shows how an individual would go about claiming the land they wanted to live on.