The term "engagement" that is stored on the Contact record refers to historical mailing action data (opens, clicks, forwards, etc.) compared to the number of messages the Contact has received. This score is commonly used to identify Contacts that are most engaged vs. least (or not at all) engaged in the mailings being received.
1. It is important to note that the engagement score for a Contact is an index or summary of combined historical actions, and not measured on a set scale (i.e. on a scale of 1-10).