Upgrades
Almost all of the system on your starship can be upgraded. Each upgrade will enhance the abilities of that system - such as increasing transporter range, or allowing the ship to travel at faster impulse speeds. Upgrades are performed by engineering teams, with larger better trained teams able to apply upgrades faster than smaller, less able teams.
Before an upgrade can be applied it has to be researched by the ships science officers. Once this research is complete, that upgrade is available to all engineering teams for all applicable systems.
As the ship gets better upgrades, engineering bots become available. If constructed these are able to assist the engineering teams with their tasks.
Engineering teams can also be used to re-purpose certain areas of the ship. For example, any of the cargo holds may be re-purposed to act as a medical triage center, living quarters for refugees, manufacturing plants etc.
Engineers can also construct structures both within the starship (such as new Shuttles or fighters) and external structures such as weapons platforms or long range listening posts.
Of course when the ship is damaged, engineering teams are used to repair this damage and bring systems back on line.