It's like having your own star port you can take anywhere in the Galaxy.
Example: When I used to go on an exploration journey, I'd have to "jump" around 95 times to get to where I'm currently exploring, which is around 6,000 Light Years away from Sol (our sun). If something happens to my ship out there, I'm a goner unless I get really, really lucky and am able to make it back.
My Fleet Carrier can jump out there in 9 jumps. If I get in trouble now, I just go back to the carrier, repair and head back out in just a few jumps max.
Another huge advantage is that the fleet carrier is indestructible. So should I be playing in Open and somebody is chasing me all I have to do is make it within range of the carrier and I'm safe.
There's a lot of advantages to having one, but they are incredibly expensive and cost millions per week to keep up. (The more features it has and the more cargo you're carrying, the more it costs.)