4sq is many things to many people. The original design was tailored to people who were going out to restaurants and bars and wanted to keep track of their friends without an annoying series of text messages. When you show up at a location, you bring up the application and check in, letting anyone on your friend list know where you're at. If you want to know where your peeps are at, just look up 'friends', and you can see that Todd and Jenny are at Lucia's Wine Bar, Dave just checked in at Bar Abilene, and Joey and Gene are at The Saloon. Should you desire to hook up with any of them, you're free to make your way any of those locations.
On top of that basic functionality are the points, badges and Mayorships. These are all behavioral rewards that attempt to make using the application more fun and interactive. You get points for checking in anywhere, but especially new places. You get badges for a certain number (or certain pattern) of check-ins, and you become the “Mayor” of a location if you're the most frequent visitor. Some people really get into pursuing and accumulating these rewards and some people think doing so is a pathetic waste of time. I'm somewhere in the middle. The one emerging advantage to being the Mayor of a bar or restaurant (other than smartphone nerd / local scenester bragging rights) is that some places will give you free or discounted swag if you're the Mayor. There's actually a bar in DC that says its Foursquare Mayor always drinks for free. Speaking of which, I need to go check in there right now.
The more recent aspect of 4sq is the perennial, all-day-long, self-stalker version. Like I said, it started out as a going-out guide for friends. The system of rewards was clearly meant to apply to being socially active in the evenings. But since it's a mostly open platform, you can add whatever locations you want (a drugstore, your office, 7-11, a public park). That means you can also check in to any location any time. This has led the self-stalkers of the world to check in EVERYWHERE they go, all throughout the day (abridged example):
8:39am – Tyler checked in to 2C Metro Bus Eastbound
8:57am – Tyler checked in to Starbucks – Downtown East
9:09am – Tyler checked in to InterQualTech Resources HQ
10:15am – Tyler checked in to IQT 7th floor Men's Room
12:07pm – Tyler checked in to Burger King
3:15pm – Tyler checked in to IQT Main Conference Room
5:35pm – Tyler checked in to Bailey's Pub & Grill
7:51pm – Tyler checked in to 2C Metro Bus Westbound
8:32pm – Tyler checked in to Tyler's Loveshack Condo
In order to pull this off, you need to have either very indulgent friends or be a celebrity. Depending on how large a following you're interested in cultivating, local broadcast media celebrities may indeed qualify. This changes significantly, however, if you have your 4sq check-ins set to automatically post to your Twitter (or Facebook) account. The Twittersphere is currently experiencing a severe 4sq backlash. Auto-tweeting every check-in – especially if you're going the self-stalker route – has become extremely unpopular of late. I advise against it. These days I only Twitter check-ins at bona fide bars where I am actually meeting friends and drinking. Anything else – Safeway, CVS, McDonald's, Office Depot, etc., should be kept to oneself. Unless you want everyone but your roommate to unfollow you.
Hopefully that makes some sense. There are a lot of other aspects to 4sq that bear some comment, but they're mostly things best understood by actually using it. The application definitely isn't for everyone – shut-ins, paranoiacs and perennial homebodies are advised to seek other amusements. For most others, though, an initial test run should determine whether it's something you'll enjoy using long-term or not.
P.S. – If you make your own house/apartment/condo/yurt a 4sq location, you are officially a lame-o.** Unless you live in a hostel or a frequently trafficked flophouse, that is cheating. It may not be a federal crime or a sin, but it's still wrong.
**This obviously doesn't apply if you're extremely charming, witty, and amusing. Normal caveats apply - if you think you're witty, you're probably not. If you think your affectations are amusing rather than annoying, that's probably not true either. It is possible, though. And in the unusual case that you are charming, witty and amusing, you hardly need me giving you advice, now do you?