Dance hold, or embrace as some people like to call it, is the way you
touch your partner. That's assuming you're dancing with somebody else, as opposed to dancing by yourself.
From the 1960's through the present day the main social forms of dancing didn't involve touching somebody else, which is really too bad. Let's face it, it's nice to touch somebody else; I saw a picture of orphaned orangutans in National Geographic once, and what are they doing? They're hanging onto each other, that's what. Since I was reading the print version of NG, I couldn't tell what music they were listening to, but I'm sure it was something cool.
Depending on the dance and the mood, you can just hold your partner's hands, which works well in salsa and swing, or put one arm around them and hold one hand and leave a few inches between the two of you, which works in pretty much every social dance, or glue yourself onto your partner, which you only do with your lover, or when you're doing the tango.
Hey, speaking of tango, let me remind you that you want body contact between your center and theirs -- depending on how tall you are, this might be touching sternum to sternum (my favorite), or solar plexus to solar plexus, or something like that. Careful, you very definitely do not want groin to groin contact! Also, you don't want to lean forward (since it throws you off balance) and you don't want to make your partner tense by pressing your head against theirs. Relax and stand up straight, and let your partner come to you; it's not very romantic to squeeze the breath out of a person. Even with somebody glued to you, it's not too hard to walk and even do interesting fun things with your feet -- you don't need to see your feet or theirs because you can feel their weight with each footstep.
So, what it comes down to is this: dance hold is cool because it combines two cool things, dancing and holding. Try this at home, it's fun.