Hello GunnerGetcha. You probably had one or more snail egg pouches stuck somewhere and didn't even realize it. They may have arrived on an aquarium plant, or in a fish bag. Depending on the type of snail, your problem resulted from either a number of small, clear, gelatinous blobs, which you could have very easily overlooked, or the culprit could have been a more foamy-looking thing, similar to a sac of praying mantis eggs.
Let me point out that not all snails lay their eggs in the water. I remember many years ago, around four decades ago in fact, when I discovered that a large snail -- an Apple Snail -- had laid such a foamy egg pouch on the inside of the light fixture where it was nice and warm.
So what is the cure for your snail problem? Personally, I really don't recommend using any chemical solutions. Even if they are used properly, they could still alter the chemical balance of your water, and possibly kill your plants or livestock, or both. If you have a beautiful aquarium which you have been maintaining and nurturing for years, it would be a tragedy to see all of your hard work and dedication come to naught.
One more natural solution is to take the time to closely inspect your tank and manually remove the snails before they reach maturity and breed. You can use a piece of lettuce or cucumber to try to attract them to one spot, perhaps even inside a jar. They will come out at night and feast on your bait. The manual approach can be tedious and time consuming, being as it may take days to get the situation under control, but it won't cost you any money. However, there is no guarantee that you will find them all, so your problem may just be repeated later on.
Another natural solution is to purchase some variety of snail-eating fish. Online sources seem to indicate that loaches best serve this purpose, being as they like to burrow into the aquarium substrate where such small snails like to hide. Just make sure that you feed your fish lightly, so that the loaches will have an appetite for the snails.
Following are two web links which will provide you with some additional information regarding snail-eating fish. If you enter the phrase "snail-eating fish" in the Google search engine, you will find many similar pages which cover this same topic:
Home Aquaria Snail Control by P.Timlin
Snails in the aquarium