It describes the need to do something that you maybe havent done for a long time . it is the short version of "einmal" you could exchange it with the word "endlich"(finally) i hope that explaines the function.

in addition to michaels answer "mal" (spoken, or casual written conversation) or "einmal" (written) makes your statement more specific and points out, that you would like to do a certain thing at a not yet fixed time. leaving out the "mal" will be more general: Very loose literal translation: Hier kann ich richtig tanzen (Here I can dance properly) Hier kann ich mal richtig tanzen (Here I can go for a proper dance)

Ich kann richtig tanzen = a neutral statement declaring you can dance properly. Ich kann mal richtig tanzen = a statement you can dance properly and is made under some premise. That premise can be just about anything, like you need to know what I'm telling you is important, but in this case it looks like the person wants to show off her newly learned skill or something. From the sentences alone it is hard to determine what the premise may be. But use "mal" when you have some premise for saying something. Ich kann mich mal mit meinen Freunden aussprechen Possible premises: I don't need to talk about it with you. I have finally learned how to express myself.(endlcih mal) ..and others... Ich kann mich hier mal in meiner Muttersprache unterhalten. Possible premises: Everyone here speaks my mother tongue. I'm back home after being abroad for so long. ...and others...