Uchiha-Miranda

llama badges are a simple and free way to contact someone. When you stumble across a deviantart page you like, you can give a llama to that person. It's a way to see "hey buddy! I'm here, I like you!" without following or faving (because, let's be honest: you don't always want to watch or fave everyone, here).
 
Most of the times, the person you gave the llama will give you a llama in return. This helps you to improve your network and to contact more people (and, to be honest, to gain some visibility)... so make wide use of llamas, just don't abuse them or your llama storms will be flagged as spam. I made some great friends with llamas, because they're like an "hello" message: informal, free and random. 

If you want to send a llama to someone, you find the llama button on the top right corner of your screen. When you're in a page you want to send a llama to, hit that button, select "llama", accept the transation and you're done. Llama sent. 

When lots of people send llamas to you, your llama badge will "evolve" multiple times, gaining an unique appeareance (I will not spoil the surprise, though). Anyway, an "higher" llama badge does not match any special privileges or stuff like that. It's just more fancy, and it proves that you got in touch with lots of people. 

There are other forms of "gifts" on Deviantart, such as point donations. Obviously, since points are the Deviantart value, this kind of gift is less common and is used to greet a special friend or in special occasions. So, keep in mind that llama can't be exchanged for points or money.  

I hope I answered tell me if you need something else, mate!