There are a few sides to this.
One is that the term "cheap plastics" is a fallacy, as most in-car plastics used for dashboards and the like actually cost pretty similar amounts whether the stuff looks and feels awful or whether it's all touchy-feely.
As far as "low quality" plastics go, there are several sides to it.
One is the feel of the material. I've never been big on this one myself - I tend to prioritize the bits in the car I actually touch, like the steering wheel, shifter, handbrake lever and so-on. The feel of the top of the dashboard doesn't really matter to me as I never touch it. But if you do, "high quality" plastics tend to have a nice texture, be a little squashy, feel solid etc. "Low quality" plastics will feel hard, scratchy, make a hollow noise if you knock them etc. Think of it like the difference between truffle-filled Belgian chocolates and a cheap Easter egg.
The next is how the material looks. Unless you're going for a gloss effect, shiny plastics tend to look "lower quality" than one with a matte finish, or a texture.
After that, it's about how it's been screwed together. This, for me, is probably most important, and the reason I don't really care about touchy-feeliness. Japanese cars from the 80s and 90s tended to use fairly hard and nasty plastics to touch, but were screwed together brilliantly. The absolute cheapest of modern cars has more soft-touch plastics and textured surfaces than say, a 1990s Camry, but the Camry feels like it'll last a million years. A car that feels like it's about to disintegrate can't be considered high quality regardless of how squishy the plastics are.
Add all those factors together, and it's why people say modern Audi interiors are so good (soft-touch, squishy, textured and well put-together), and say, a 1990s GM product is so goppingly awful (as hollow as a coconut, hard, scratchy, usually an unappealing shade of grey, screwed together with the precision of a stampeding elephant).