The main advantage of a computer is that it gives you a dive planning feature which allows you to plan your bottom times for various depths on repetitive dives, for air or various nitrox mixes.
For relatively shallow dives in the 50 ft range, you can probably ignor this. But if you are diving in the range of 75 to 100 ft or more, this is really nice. You press a button, and there is it, in real time. If you want to wait longer, you can input more planned surface interval time, then press a button, and there is the new number.
The second main advantage of a computer is that it calculates a very precise average depth per dive. This allows you to track your SCR.
The third advantage is that they have an ascent rate monitor built in, and they will beep and thus warn you to slow down if you are ascending too fast.
The final advantage, as others have said, is that it records a lot of data for you, such as max depth, current depth, dive time, profile, water temp, etc. This info can then be transferred into your log easily.
For old salty divers, the computers take the place of the watch and the depth gauge and eliminate the need for dive tables to plan repetitive dives. I dove for a long time with a watch and an analog depth gauge, until the computers became very reliable and sophisticated around the late 1990s. Then I finally bought a SUUNTO.
Boat captains, these days, look for 3 things most often on divers: (1) a surface marker buoy rolled up and attached to your B/C-harness; (2) a dive-alert horn attached to your LP hose; and (3) a dive computer. If you have all 3 then they are usually pretty happy with you being on their boat.
When I dive trimix tech deco, I switch the computer into to gauge mode, attach it to a bottom timer as a backup, and use that for square profile deco diving.