For the purposes of a discussion of fermentation in the context of brewing and distilling, plant polymers most especially starch is going to be our primary concern here. Starch is a form of energy storage used in seeds and tubers. Seeds want to store energy so that when they germinate there is enough energy to fuel the growth of the sprouting plant. Like the yolk of an egg, the starch provides the calories to get growth going, during the phase before leaves have appeared for the manufacture of energy sources from photonic energon particulates (sunlight) and carbon. Once the plant has leaves and roots it no longer needs that starchy internal energy source as it can make its own.
Starch is a chain of glucose molecules. Glucose is the simplest of sugars. It's a 6 carbon ring with some OH groups hanging off the sides. Those OH groups are active groups called alcohols in organic chem. If you strap 2 glucose molecules together you get maltose, a disaccharide that gives malt shakes, malt balls, and many beers their unique and amazing flavor.
Keep strapping a few of them together and you get dextrins, short chains of sugar that cause thickening but not much sweetness (body and mouthfeel in beer). Strap a couple thousand glucose molecules together into a long chain and you get a starch molecule called amylose. Add some branches and you get amylopectin.
These polymers are found in grain and starchy tubers. They are great energy sources for the seed/sprout...and of course for yeast. When we set about making beer or whiskey, job number one is to get the starch freed up from the structural polymers and containment vessels in the material. We need to free the starch because the plant has encased it and kept it dry so greedy microbes can't get access. If we get the starch freed up and into water, we can use enzymes to break it down into simple sugars that yeast can metabolize and make into alcohols and aroma/flavor active compounds.
The other plant polymers made up of glucose are things like cellulose which can't be broken down as easily. Cellulose is what the supple green plant tissue is made of in a new bud or leaf. There's lots of energy stored here but it's really hard to liberate as the bonds holding the glucose molecules together are much more stable. It's sort of like the nuclear energy thing. The amount of energy in a bowling ball is greater than all of the bombs we've ever set off. The thing is that the bonds holding the material together in that ball is so great, that we don't have the ability to liberate it without investing so much energy it's not worth it. Cellulose has to hold plants together where starch has to fuel them...so it's meant to be broken apart. Cellulose is exposed to all of the airborn microbial life our abundant Earth has to offer and is pretty resilient.
Lots of plants have free sugar available without enzymatic treatment. The white powdery layer on the outside of a grape or apple has a good deal of yeast in it. Yeast, like bacteria, are ubiquitous meaning they are very literally everywhere around you. This is why you can leave flour and water out and start a bready yeast culture for your sour dough starter. Distillers used to do the same, capturing live local cultures and testing the flavors of their particular exudations (booze is pee...call it sweat if that makes you feel better). These days we most often use purchased or cultured yeasts, some are using a combination of both.
Tubers (potatoes) are really the same deal although it's a bit simpler to liberate the starch from a potato. Once the starches and sugars have been consumed and distilled off there is a good deal of material left over. Some of this goes to feed animals, some goes to biodigesters (to produce biogass that can go into boilers like natural gas) from another kind of fermentation, some of it gets composted, some of it gets spread directly on fields.
If you're starting from grapes or fruit it's really much simpler as you don't even have to add yeast to get things going, although it's advisable to control your culture for consistency's sake. When breaking down starches it's inevitable that not all of the starch will end up as the simplest sugars (glucose and maltose). Even slightly longer dextrins (3+ glucose) are difficult for yeast to do anything with but there are bacteria that are happy to get involved. LAB (lactic acid bacteria) love them some dextrins but they produce lactic acid. Some distillers love this some not so much but regardless it needs to be controlled. This isn't really an issue in fruit as the sugars are already simple so the yeast are in heaven. There are certainly infections that can occur later on if conditions aren't sanitary.
That's all I've got for plants, not that this is comprehensive but it's the basics.
Power to the Plants!