The United States is an at-will employment country. At-will employment means that your employer can fire you for (almost) any reason and you can quit whenever you like. Companies, of course, modify this relationship with contracts, but the government interferes minimally in employment relations. The question is then, how do you know if you were wrongfully terminated?
Wrongful termination results in three distinct situations. First, the firing is against public policy, second, when the termination violates an actual or implied contract. Finally, a termination is wrongful when it violates the covenant of good faith and fair dealing.
Terminations against public policy are the ones that make the news and are the only ones with laws on the books discussing them. For example, under federal law, you cannot be fired for your race, color, creed, sex, or because you have a disability. Most state laws expand these rights to include gender, sexual orientation, HIV-positive, and other descriptors. A termination in violation of public policy can result in statutory damages (damages mandated by law to punish conduct) and civil damages (money to replace the income you would have earned).
Terminations violate a contract when you are fired for a reason not permitted in the contract. Most employers now have employee handbooks. The handbook is what the majority of wrongful termination suits turn on. Usually, your employer must obey certain procedures or can only fire people for "just cause."
Finally, the covenant of good faith and fair dealing means that the employer cannot fire you without just cause. Just cause means they can articulate a reason to justify firing you. For example, chronic lateness.
If you believe you were wrongfully dismissed, then may want to speak to an attorney; you could have an actionable claim for compensation. If you were wrongfully terminated, you are entitled to compensation for the loss of your job and possibly future income. A lawyer can go over the various legal method by which you can pursue compensation for your injuries. You don't need to fight this out on your own; a lawyer can have your back.