This thread is intended to be a discussion. Please don't post image responses, explaining your thoughts on the matter with words always leads to a better discussion. Thanks!
We all know what happens to our characters when we're playing them, that's easy. There's a whole other part to their lives, though, that happens when we're not watching. They're not simply on pause while we're off living our lives, or they shouldn't be, because that's a fast track to a stagnant character. They have work, classes, hobbies, and an entire school to roam around in while you're offline. I've observed on my own and heard from multiple people that it's frequently difficult to remember to consider what your character was up to, either in day-to-day RP or over breaks when you year them up.
Taking this into consideration will help create RP when you log in. Imagine that you determine(perhaps randomly by rolling on a list of possible events, or simply picking an idea that sounds like fun) that your character had a run-in with that professor they just can't stand - Aurora Sinestra! Who does that lady think she is, anyway? She doesn't help you at all if you're falling behind, that's why I'm barely scraping by with an A in that class. Right there, you've got options - maybe you can just have a good vent session with some good friends, or you might even open up RP to have another student tutor your character in their weak subject.
It can also help you change your character's mood around. Maybe your character has had a lousy week, and you decide something pretty awesome happened that day(last minute schedule change meant they got Slughorn for potions instead of Snape, and he decided to let them brew cherry soda in class as a treat!). Or maybe your character is always extremely cheerful, but something awful happened, and they're in tears when they enter the entrance hall. The latter is also a good way to have RP created, as other characters would be curious what happened. Of course, this comes with a caveat. Be careful about using stuff like this to try to OOCly force your character to be cheerful. Sometimes life just sucks, and your character is going to be gloomy. RP it out with their friends, and it'll work out better than trying to toss random good things their way to cheer them up.
Summer vacation RP earns a special mention, because it's a pretty weird timebubble situation, but also extremely important. I always take some time to think about what my character did that summer when I year them up. How were relations with their family? Are they still fighting with their mum? Did it get worse this year, or better? Also, as characters get older, it's good to consider if they had a summer fling with a NPC of your devising, or took a part-time job over the summer to save up money, among other considerations. This is 2-3 months of their year, a lot can happen in that time. You don't necessarily have to work everything you determined into RP, but it's extremely helpful to know that it was a thing that took place. For example, Sam had a job waiting at a restaurant the summer before his 6th year, and things went down. Almost all of the things have not been mentioned in RP at all, yet it's definitely effected his reactions to RP events.
For discussion, how do you handle this for your characters? Do you have any tips for coming up with good off-screen RP, or for working your off-screen RP into your on-screen RP(aka, the stuff we do most of the time that's considered "RP")? Does all of this sound just like the mad ramblings of a head DM who didn't get nearly enough sleep last night and you want to ask questions? Go right ahead, I want to hear your thoughts about this, and maybe you'll inspire the creativity of another player.