A third-party service provider is an unaffiliated business that provides services to another business while maintaining separation from the businesses as a contracted entity.
For example, many ecommerce stores use third-party service providers to process and manage payments. The third-party payment processor provides a service to the ecommerce stores based on a contract between the parties.
The IT field is common for third-party service providers as most businesses outsource server maintenance, security and other complex technical services to an experienced IT company.