During my first consultation with people who are interested in filing bankruptcy, I always explain this very important subject of "exemptions". Let's see what exemptions are and why they're important.
In a Chapter 7 bankruptcy, for one that gets rid of your debts quickly and the one that most people want, the trustee assigned to your case gets to take your assets (your "stuff") and sell them and give the proceeds to your creditors. Or in the case of cash or bank accounts, just take them from you to give to your creditors. EXCEPT for what you can "exempt", which you get to keep. That should take care of why exemptions are important :-)
What can you exempt? It depends of the state you've been living in for about two years. In California, if you need to exempt (protect) equity in your home, that exemption is from $75,000 to $175,000 depending on your age and other factors.
Also in California, if you don't need to exempt equity in your home (maybe you don't own your home), you get a "wildcard" exemption of about $28,000 that you can use to exempt anything or multiple things. You also get exemptions for specific things like house furnishings and cars and retirement accounts. Some of these exemptions have specific amounts and some are unlimited.
As can see, exemptions are not only important, they are not simple. This article is only a brief introduction. Your bankruptcy attorney can explain this very important subject to you based on your specific situation.