I’ve seen a few gyms now that have an area that they refer to as the functional area. What is actually meant by this?
The selling point of "functional fitness" is that it's comprised of exercises that make you more fit for everyday life. They are supposed to train natural movement patterns like squatting, pushing, pulling, twisting, and overhead so that the body is easily capable of handling these movements when the need arrises.
The idea is that people typically don't need to bench press a barbell in normal life, thus that exercise is not considered "functional". But sometimes you may need to throw or catch something, so throwing a medicine ball against a wall is more "functional". Performing this exercise safely in a controlled environment would then prepare you for the event you need this ability in the wild.
There may be some validation to it. For example, grip strength is a good biomarker for longevity. One reason for this is because it reduces your chance of severe harm from falling which causes thousands of deaths per year. Basically if you have good grip strength, you can most likely grab something and prevent yourself from smacking your head on the floor. So based on this logic, pull-ups would be considered highly functional because they train you to grip and hold your bodyweight while also training you to pull yourself up.
As you probably have noticed, there's no set definition of what's considered "functional", and a lot of gyms and trainers have taken it upon themselves to come up with the most wild things to differentiate themselves from others. Very often this involved taking some normal exercise and making it as unstable and dangerous as possible (anything on a bosu ball for example). Other times they simply take a normal exercise and modify it to use some special equipment with the promise that it yields faster/better results.
There's no reason to believe that battle ropes or medicine balls would yield better "functional" results then standard barbells, dumbbells and kettlebells. These are tools that have their time and place, but their's no evidence to believe that using this equipment would be better. There's also no reason to believe that using traditional equipment wouldn't prepare you for everyday life. The body doesn't particularly know or care what you're moving. It just knows that for some reason you need to move it.
Train a squatting movement. Train a pulling movement. Train a pushing movement. Train a twisting movement. Train an overhead movement. Stay the hell away from bosu balls. You'll go far.