First post of this explains it (note, they're using the term "online" pretty liberally in that post. As far as I know you're not actually online with their severs at all):
http://forums.undeadlabs.com/showthread.php?541-Faq
But basically it tracks how long since you last played and adjusts the game as if the world were persistent and online and you were absent. Don't play for a day, your small clan continues to evolve. You come back to find that relationships have shifted slightly, resources have changed, the side missions available might be different. This is front loaded so that not playing for 1 day generates significantly more change than what occurs in the last week of four weeks of not playing.
The direction of your little society while your not around depends upon the state they are in when you stop playing. If things are good you may have some new resources and your vehicles might be repaired. If things aren't good, tensions might be higher and resources might be slightly lower. Or your base is slightly damaged from a recent zombie attack.
It's a weird concept to get used to. You may like it or not or it may not even be drastically noticeable to you. Depends on the type of player you are. I'm the kind of player that can't play WoW because if I'm playing, I want to be bleeding edge raiding every night. It's all or nothing (and so its nothing. Growing up sucks).
Just to emphasize, I've never come back in and found the game drastically different. Meaning none of my characters were dead, people weren't starving, etc. It's subtle. Leave the community in bad shape, don't play for a week and it will be in a little worse shape when you get back.
Also, I didn't mention in the first post but the character system is pretty good. Characters develop into roles nicely (based on the rpg-lite system that drives character development) much like you would expect in a real world post-apocalyptic situation (think how characters develop roles in the Walking Dead. Like that).