Perhaps I can shed some light on why we ferment tomato seeds (and eggplant and cucumber). I am a 6th generation heirloom vegetable seed saver and seed producer.
Basically, seed fermentation is just the process of letting seeds soak in their own juices or “gel” until the juices start to show mold. This is a sign that fermentation is going on. What the fermentation does is turn the tomato’s sugars to alcohol that then destroy a germination inhibitor that’s natural to the seed. Why has the plant evolved with reproductive seeds that have a component that inhibits the process? To prevent them from germinating too soon. Think of a tomato left to its own devices in nature. The fruit matures and falls to the ground. Without the inhibitor — and with everything it needs to sprout — the tomato seeds will start to germinate in their own juices even before winter has set in. The inhibitor sees to it that they don’t.
The fermentation process also has other benefits. The alcohol and other products produced by fermentation will kill off any seed-borne illnesses that your tomato seeds may carry. It's also a chance to go carefully through your seeds and pick out any that are just no good AND it also kills Clavibacter michiganense pv. michiganense a Bacteria that affects the unfermented seeds.
Most important is to know your tomato, even wise growers can mix up tomatoes after they're picked, so be sure to track the ones, usually heirlooms, that you want to save seed from. Fermenting the seeds is easy. Choose the best healthiest looking tomatoes for their superior genetic traits. One tomato of each kind will do most gardeners unless you’re growing rows of tomatoes or want to share seeds to neighbors and friends. Slice them in half horizontally and scoop out the seeds with their accompanying gel into a glass jar. Leave it in a not-too-cool, dark place for a day or two. Check it regularly. As soon as a mold or scum covers the top it is time to clean your seeds. (Leave too long and your little seeds may sprout or rot).
What you’re doing is creating the same conditions the tomato would have if left to its own devices. When the fruit falls to the ground, it slowly rots - ferments - with the seeds inside. Weather, in the form of rains, drying sunlight and winter, will eventually decay the fruit to nothing, leaving behind only the seeds. But during the tomatoes first days on the ground after ripening, the fermentation process occurs naturally, there is also a better strike rate when you come to plant them.
Once the mold starts to form in 2 or 3 days, scoop it off with a spoon, place seeds in a kitchen sieve and very gently rinse them off under the tap until all the gel is gone and just clean seeds are left. Let them dry on a plate or tray somewhere where its warm (but not too warm) and dark with good air circulation, and run your hand through them every so often to turn them to dry thoroughly. Be sure to keep your seed labeled all through the process.
When they’re fully dry, I usually wait 1-2 weeks to be sure, store them in a cool, dark, dry place inside a tightly closed LABELED glass jar, NOT in a hot garage or kitchen drawer near a stove. Then, at the tail end of winter, 6-8 weeks before the last frost, they will be ready to start off under cover ready to plant out in spring. The reason we use a plate or tray is so the sees don't stick and pick up bacteria from the paper. Many brands of paper towel use toxic chemicals and bleach during processing and shouldn't be placed next to seeds - just a tip if you are trying to grow healthy organic plants.
Hope this has explained the science behind the reason we ferment some seed types.