In short, a SIN is character's general physical information (i.e. DOB, metatype, etc.) and some other data (criminal records and whatnot) about them stored in a database run by a nation or corporation. In addition to this use of the information, SINs are often used for advertisers and financial transactions, by being linked to a credstick or commlink, allowing for their owners to be tracked but also experience a highly customized lifestyle that theoretically improves their quality of life.
Pages 366-368 have the rules for the mechanical functions of a (fake) SIN; essentially, your SIN is theoretically broadcast from your commlink at all times, but you can set it up to use any of your SINs, or even just not to broadcast (though this gets you in trouble in the uber-secure areas). As a general rule, unless the player has already presented another SIN, they may choose the one they want to use when questioned/checked/otherwise harassed about handing over a SIN. The quality of a SIN determines how "real" it is without, of course, being your normal SIN, unless you're SINless.
The point of the SINner negative quality is for three reasons:
The first of these is pretty simple; it's theoretically possible to look up a person's SIN using biometrics, so if you get taken in for doing something, you need to consider the fact that you'll want a fake to present before they find your real identity. Usually, unless it's an obvious fake, that sticks your (hopefully clean) fake SIN with the criminal record, at which point you can ditch it and get another.
Taxes, of course, are one of the two things which are certain in life, and one of the upsides of not having an official identity is that you also do not wind up paying taxes; some of this is offset by the fact that the SINless may have to pay for public services a SINner can access free, but as a general rule a 400 nuyen bus pass is still cheaper than 3600 a year in taxes.
And scrutiny is the largest one. The SINless distrust SINners, especially corporate types; it's one thing if you're born into the squalor of a ditch in the UCAS but your parent(s) happened to have a SIN or two between them and got you one, but if you've got a high-level corp SIN you're essentially looking at being set for life with a silver spoon, unless you do something horrible. Also, while it's not technically scrutiny, people with corporate SINs often find themselves "scouted" by rival corporations or even other branches of their own corporations, and extractions can be dangerous for everyone involved.