When a person is obligated to appear in court (for any reason) and they do not, the judge can choose to issue a warrant for their arrest - this is known as a "Failure to Appear Warrant," or "FTA."
The most common FTA's in the US occur when people neglect to show up in court regarding traffic tickets. Of course, anybody committed of any crime which requires a hearing is subject to receiving a failure to appear warrant. You can also receive a warrant for not showing up for jury duty when you are assigned to appear or not showing up for a civil lawsuit hearing.
In some states FTA's are actually treated as misdemeanors - this means that you can actually receive more charges for not bothering to show up for a hearing. Since most misdemeanors carry a maximum jail sentence of one year obviously this is something you should take very seriously.
How long do Failure to Appear Warrants last?
There is not statute of limitations on failure to appear warrants. If you have an outstanding warrant from decades ago don't assume that the warrant is no longer standing. States will rarely extradite for failure to appear (but often will if the original charges are more serious).
How do you get rid of a Failure to Appear Warrant?
Of course the details of your situation are unique and you should contact an attorney if you have a failure to appear warrant. The attorney will probably contact the court or police department (depending on your jurisdiction) to give an explanation for your failure to appear. In general, when you show up for the court appearance the warrant will be dropped.
If your failure to appear is a result of not showing up for jury duty then you may be subject to more jury duty assignments. The judge can also issue a bench warrant (but in practice this is rare). Also, you may have to pay the court a fine.
What if I'm innocent?
Remember, a FTA warrant has nothing to do with the details of your case. Even if you are found not guilty or the case is thrown out for a lack of evidence you are still expected to show up for any and all hearings related to your case. Even though your original case may be dismissed the FTA charges may remain.