Speaking as someone who's in the plastics business, who is NOT in California, but HAS read up about this...
It will outlaw single-use bags starting in July 2015 at large supermarkets and grocery stores, and in 2016 at convenience stores and pharmacies.
You won't get fined for using them; stores just can't give them to you when you make a purchase. You'll probably get a paper bag -- if it's small enough item, maybe you just won't get a bag(?) -- or you'll have to bringing your own re-usable fabric bag(s) everywhere you go. California is trying to prevent waste plastic bags from entering the ecosystem, especially into the oceans.
Unfortunately, this is a behavior problem, as people aren't disposing of these items properly. (Now, whether or not (a) digging a big hole, (b) dumping everything in, and (c) covering it with dirt constitutes a proper means of disposal is a topic for another discussion.)
Some U.S. studies have shown that even when plastic is removed from the equation, the amount of litter remains somewhat constant; it's just that the material make-up is different -- people continue to litter, but now it's paper bags instead of plastic bags, for instance; the behavior doesn't change, despite the plastic ban.
But I suppose it makes some people "feel good"...
Other municipalities are charging a minor fee (5¢ / 10¢ per bag, for example) at stores in an attempt to penalize their usage.
Looks like there's enough signatures to try to put this on hold if it makes a referendum on the 2016 ballot:http://www.nacsonline.com/News/Daily/Pages/ND0105154.aspx#.VKs2lHvCZVc(I guess due to the peculiarities of California state law, once it makes it to the referendum, the measure is put on hold till the people vote on it.)
