A subcontract is a legal agreement to do part of a larger job. A worker or small company usually signs a subcontract with a larger company.
As a verb, subcontract means to hire a person or company to complete part of a job. An example might be a construction company that's been employed to build a house deciding to subcontract all the plumbing and electrical work out. In other words, they are paid for the entire job, and then they pay a plumber and an electrician to do specific parts of the job.