Okay, here's a bit more explanation than perhaps is really necessary but I find if I understand the "why" something is done a certain way it makes it easier for me to remember how to do it.
The reason that base nutrients come in 2 or 3 parts in liquid solution starts with the fact that water is heavy. The heavier something is, the more it costs to ship it. The bigger a jug is the more room it takes up on a shelf and that means more shelf space, more storage space in the warehouse, and so on. All that costs money. So the smaller and the lighter something is the better it is for the customer.
To get the jugs smaller and lighter, they have to put cram more nutrients into the same liter bottle. But you can only do so much cramming before no more will "fit". If you go too far the nutrients start to grab onto other nutrients in the solution and bind together as a insoluble salt. It's like how you can add salt or sugar or something to a glass of water. It will dissolve but if you keep adding more and more you'll reach a point where no more will dissolve. Well when you start talking about fertilizers you're talking about a lot of different salts in the same glass of water and some of the ingredients in those different salts are strongly attracted to each other and want to hook up. If you don't have enough water to keep those ingredients dissolved they bind up, fall out of solution as crud at the bottom of the bottle, and won't dissolve back no matter what you do.
Obviously that's bad, since your plants can really only consume nutrients in the soluble liquid form. If they bind up, they're useless.
A full nutritional base nutrient contains enough different nutrients that if you have everything in one bottle you have to have a crapload of water to keep them all soluble. Buuuuut, if you divide them up so that the ones that are most strongly attracted to each other are in two or more different bottles, you can use a LOT less water, make the nutrients a lot more concentrated, and give the customer a product that costs less to ship to the store, takes up less room on the shelf, and thus costs a lot less at the register (not to mention being a hell of a lot lighter to lug home).
But if you mix an A & B nutrient together without more water, you'll instantly get those highly-attracted ingredients hooking up and falling out of solution.
So what people mean when they say you can't mix them together is that you can't mix them together at the concentration they come at in the bottle.
You DO WANT to mix them together. The way you do that is in water. So say you're making up a gallon of nutrients to give your plants. You get your gallon jug, fill it with your water, and then you add the nutrients to it one by one. So you'd measure out the right amount of A, pour that into the water (avoid splashing), and then stir it up really well. Then you measure up your B, pour that into the water that already has the diluted A in it, and stir that up. Because you've diluted each thing before you added the next, you don't have any of the ingredients "hot" enough to grab onto something else and drop out of solution.
Once you've mixed everything you're going to use into the jug, you feed your plants - again, avoid splashing. If you get nutes on your plants you can "burn" them.
