A direct hire refers to a situation where a company who intends to hire a candidate offers them the job directly.
Companies may utilize the services of an employment agency to find the right candidate for a vacancy, but in a situation where a direct hire occurs, the company that is going to employ the candidate is the one that actually hires them. See more on employment agencies here. The candidate is an employee of the company that performed the direct hire, not the employment agency.
As a direct hire involves action and investment from the hiring company, direct hires are usually made when filling permanent roles as opposed to a temporary or contract-to-hire roles.