An LLC is a legally distinct entity from your person. Basically, if your LLC is sued, and you lose, you can lose only what you put into your LLC. Your personal assets are untouched.
A very sophisticated plaintiff may try to get around this suing both your LLC and you personally. (I've done this myself.) Even so, if you are careful to keep the business of your LLC separate from your personal business (no commingling of assets, no use of your LLC to pay your bills, but only a salary), then the law will often absolve you of personal liability for the "actions" of your LLC.
The reason I warn against "commingling" is because if you do this, you can lose the protection of the LLC as a separate entity, and become personally liable for what the LLC does. This is known as "piercing the corporate veil."
If you have home rental operations in more than one state, you may want to establish LLC's for each state. That's because some states are more tenant- and other states are more landlord- friendly than others, meaning that you may want to defend yourself differently in one state versus another.