Downtime
Downtime, in RPG terms, can basically be described as what your character is doing in between normal sessions.
What is Downtime
After a normal run, you write your characters "downtime" and send it to the GM. The Downtime explains to your GM what your character is getting up to after the run, but before the next one. It helps to tie the runs together, adds personality to your character and gives more interesting plot hooks for the GM to work with.
So what should I include?
The minimum you should include on a downtime is anything needed to explain any changes to your character. For instance, if you have spent Karma upping your firearms skill, you could have your character going down to the firing range for practice. If you have upped a more intellectual skill, you could have your character hitting the books. The other key thing you should include is purchasing items. Buying stuff in SR can be tricky, and anything you want to buy between games should be put into your downtime. A lot of the time, it'll be fairly simple: at worst just a matter of time. Some of the time, however, there could be entire runs based around the fact that your character is trying to buy something. Fun stuff. Ideally, however, you should include other stuff on your downtime. Maybe your character went to a gig, or the theatre. Maybe he just hung out at home watching sport trids and drinking beer. Has he been indulging his hobbies? Has he been hanging out with his mates? Not all of this has to be character progression or stuff that has no immediate impact on the game, mind. If your character has buildy skills, you could use this time to build things. Hackers can write programs, mages can work on spells, faces can do a little networking. Be imaginative.
What shouldn't I do?
There are very few specific things that you shouldn't do. As long as its within the rules, you should be fine. What you should't do is submit a downtime along the lines of "I gain this skill and buy a new gun". It'll just be sent back with a reply of "how?"