An entity is a type of thing a company tracks in its system - most often a client, a job, an invoice, a task or a document. Each entity has its own table in the database and its own set of fields (a client has a name, a registration number, a contact person; a job has a deadline, a budget and a status).
The difference between an entity and one of its records is the same as between a category and a single item in it - "client" is the entity, while "Acme Ltd." is one specific record in that entity.
When designing a business system, picking the right entities is the first step: deciding what the company needs to track separately (and connect through relations), and what's just an extra field on another entity. A service business will typically need entities for client, job, service visit and invoice; an agency more likely client, project, task and time entry.
Related: A data model that grows with the team, What is a record, What is a relation.