So called Ultra Low Cost Carriers (ULCC) like Frontier, Spirit, and Allegiant do not participate in interline agreements. An interline agreement allows one airline to transfer a ticket to another airline in the event of a cancelation or extreme delay. When things run smoothly, interline agreements are irrelevant. However, when problems arise, they can save you hundreds of dollars and/or many hours of frustration.
When a ULCC cancels a flight, their only obligation is to either refund your money (which may take days) or put you on the next available flight. The keyword in the sentence is "available". During a busy time, the next available flight might be the next day or even later. Typically, ULCCs will not pay for any additional costs incurred by the delay. That means you're on the hook for meals and/or hotels until they can get you on a flight.
The only way I'd fly on one of these airlines is if I had stellar travel insurance. Without that, you're gambling. It just takes one cancelation to negate any savings. If you have to get home that day, you're stuck paying the last-minute fare on another airline.
[Note: Southwest is another airline that does not use interline agreements. Due to Southwest's size, the lack of interline is not much of an issue. Southwest has 735 planes serving 99 destinations. In comparison, Frontier has 69 serving 62 destinations. As such, it's much easier for Southwest to recover when a flight gets canceled. They can more easily find a different plane, cabin crew member, or alternate routing to help get you to your destination.]