Context can be seen as a bucket to pass information around. It is typically used to pass things not necessarily tied directly to a method call, but could still be pertinent. A layperson way of describing it might be "stuff you may care about".
For e.g. if you were writing a service to update a value in a db, you'd probably pass in the record id, and the new value.
If you want generic interfaces, you may also define a context to pass, such that the service can perform arbitrary business logic. So you may include a user authentication, the user's session state, etc... in the context, as the service may perform additional logic dependent on these values.