Almost everything in OpenVPMS has an 'ID'. This is simply a number and it is unique - ie if there is a customer with ID 1234, then there cannot be a patient with ID 1234. Most of the time you don't need the ID. However, it can be useful in identifying the exact patient, customer etc, and hence it is normally printed on things like invoices. Thus if there are two Mr Smith's each with a dog called Rover, the ID will identify which Mr Smith and which Rover.
An Identity search includes a search of IDs. Thus, when you search for say a customer with an Identity 1234, those found will include those with ID's starting 1234.
Although almost everything has an ID, the ID is normally not displayed unless there is a mechanism to search for it. Thus it is displayed on the on the customer, patient and supplier information screens, but not on the Workflow|Scheduling screen - although each appointment does have an ID.