We are all the same underneath or clothes, so for many nudists, being naked in a social setting is a way to more closely connect with other people in that raw, natural way that is free from all the status signals that certain kinds of clothes can give off. To a nudist, stripping away all of the artificial textiles can lead to closer and more respectful connections between people. As a result, nudists tend to be more accepting of many different body types.
2) Communing with Nature
Many nudists feel that part of connection with nature is tearing off barriers like clothes. Nude beaches are very popular for this reason; it allows people to feel a closer relationship with one of nature's more powerful forces—the ocean. In a sense, going nude is becoming like our primitive ancestors who had a closer connection with the natural world.
3) Living a Healthy Life
Many nudists believe that being out in the sun in ones natural state is important to keep healthy, and that the sun has healing properties. This goes hand-in-hand with the idea of coming together with nature, and because of this many (but not all) nudists adhere to healthy eating practices or avoid non-natural foods as well.
For some nudists, it's not that complicated at all: They just like the feeling of not being physically confined by clothes. If you really think about it, does it actually make all that much sense to wear clothes when we jump into a pool or swim in the ocean? Normally, we don't wear clothes to take a bath—and in fact, in many cultures, people go nude when bathing in public hot springs—so many nudists feel that there's no reason other than an artificial sense of social modesty to wear clothes when swimming.
5) Finding a Community
All in all, nudists tend to be more accepting of many different kinds of people (though of course, as with any group, not all of them are like this). For some individuals who choose to become nudists, others of their kind provide a safe and healthy social environment for them to partake in. One can forge many close relationships will people since so many barriers are down.
Now, it's worth noting that finding romantic relationships specifically in such a community can sometimes be a challenge, or it at least requires something of a different mindset. Since overtly sexual activities—and especially lecherous staring—are generally frowned upon in nudist communities, and in fact go against many of the things nudism stands for, you may have to take a more subtle approach if you find another nudist that you're interested in. In mainstream society, we get to know someone first, and then see them naked; obviously, it's the opposite in this case.
Hopefully this clears up some of the questions you had about nudism in your mind. Remember that you don't have to join a club or do anything special to become a nudist—you were born nude, after all!