As the game states in the Captain Information screen, the captain's abilities give a bonus to performance. The way this functions is simple: each point in a captain ability is equivalent to one point in each of the officer abilities related to that specialty. E.g. a captain with a Support ability of 40 gains an effective +40 to their ship's Maintenance, Repair and Engine ability totals. (This means that a captain with a good Support ability doesn't need to have a Repair Crews item or officers with Repair ability in order to perform basic repairs.)

I've done enough testing to believe I can pinpoint the exact effect of two of the abilities: launcher ability reduces torpedo reload by 0.05% per point (i.e. you get 1% reduction for every 20 points), and engine ability increases engine boost duration and submarine oxygen supply by 0.1% per point (i.e. you get a 1% increase for every 10 points). Keep in mind that this is then modified by morale - I tested using a crew with a morale between 115 and 120.

For example, my current crew has 220 Engine ability. My captain's Support ability of 40 is then added to this for a total of 260 points, resulting in a 26% total increase to boost duration and oxygen supply. If I had the corresponding amount of points in Launcher ability, the reduction in reload speed would be 13%, provided I can maintain a high level of morale (which so far has not been a problem).

I don't know know what the officer level cap is, but it's possible to train a crew to a higher level than mine, and after you hit the cap, you can, if you have the credits/gold, still improve your officers' maximum morale via Advanced Training for a further boost. So as you can see, the bonus from officer skills can be very significant.