A mortgage contingency is essentially a way for a buyer to get out of an offer with no penalty if they decide that they do not want to buy the property. This is important because the seller may reject other offers to accept the one they like. Should that buyer back out, it can harm the seller financially.
For example, perhaps the most common contingency is that the purchase is contingent on the home passing inspection. If the inspector determines that the home is unsafe or has major issues, the seller can then cite this new information as a valid reason to back out of the purchase.
That does not mean they always will. They may simply alter the price to reflect the needed repairs or they may still offer the full price as long as the seller makes the repairs first.
The contingency is a safety net, so why would anyone ever waive it? The most common reason is just to make the offer more attractive to the seller in a hot market. If they’re offering cash but they know a lot of other offers are going to come in, they may take a chance, risking that the home will fail the inspection, in order to jump other buyers who refuse to do so. Even for a home that is in good condition, the seller may be more likely to take an offer without a contingency just because it’s easier for them and they know the sale will go through.
In any real estate transaction, make sure you know exactly what options and legal obligations you have.