The term firm fixed price contract refers specifically to a type or variety of fixed price contract where the buyer or purchaser pays the seller or provider a fixed amount, and that this particular set amount will not waver of vary under any circumstances whatsoever, such as in instances in which unexpected costs suddenly arise and the provider may have to expend additional resources. There are benefits of this type of contract to both the buyer and the seller. To the seller, it is beneficial because it typically allows for the seller or provider to charge a higher base fee. Since there is no chance of that number growing, it is not likely to draw the sticker shock that it would otherwise to have a slightly higher number. However, for the buyer that also provides a very tangible benefit. Even though you are paying a slightly higher amount up from, you are purchasing with that peace of mind, peace in the knowledge that this price is not going to chance, will not go up under any circumstances.
This term is defined in the 3rd and the 4th edition of the PMBOK.