They are popular because many are easy to care for, and there are many types of cichlids such as apistogrammas, discus, angelfish, ect. that have a variety of colors. I believe that's the main attraction to them; how colorful they are. Take African cichlids for example, there are tons of different types, which range in sizes from 0.5-25" basically, from aquariums 10 gallons and up, there's an African cichlid perfectly suited for one.
Angelfish have been a popular fish for quite a while, many people like them because of their coloring and just the way they look in general, they're basically top 5 in popularity for freshwater aquarium fish, and African cichlids are maybe in top 10, top 15, angelfish alone bring up the overall popularity for all cichlids.
In regards to your question whether or not they're intelligent; they are fairly intelligent, but overall for many people I think the major attraction is how interactive they are; with oscar cichlids, Jack Dempsey's, ect swimming to the front of the tank whenever they see their owner, many people describe them as water dogs. They do not necessarily know when they're going to be fed, they just generally gather to the front of the aquarium, in hopes to be fed, or they may think it's feeding time. However, this behavior is far from exclusive to cichlids, tetras do it, many types of catfish do, rainbow fish, betta, gourami, spiny eels, ect.
As I said, I think the major appeal is the coloration, the cichlid family is huge, there's African cichlids, South Americans, Central Americans and New World cichlids, so generally, there's something for everyone's preference and taste.