You trade art with someone else. You draw something for them, and they return the favour. Thus a 'trade'. It's usually done to requests, like you draw someone's original character [OC] or a fanart of their favourite character, and they do the same for you.

I realise how strange I must be, commenting on people's comments on other people's profile pages xD

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Common sense and a sense of humor are the same thing, moving at different speeds. A sense of humor is just common sense, dancing.