As someone who's just spent half an hour reading Wikipedia thanks to this thread, I can now dispense a summary of what I read to make it feel like I didn't just waste a chunk of time I should have spent in bed by wasting another chunk of time I should be spending in bed.

Fats are made out of fatty acids, which are carboxylic acids with a longish carbon chain. A saturated fatty acid only has single bonds between carbon atoms, a monounsaturated fatty acid has a single double bond somewhere in the chain (and these are sometimes things that turn into buzzwords, e.g. omega three oils are ones where there's a single double bond three along from the end of the chain), and a polyunsaturated fatty acid has more than one double bond.

Single bonds in a carbon chain can only be one way around, so you don't get isomers of saturated fatty acids, but double bonds in a carbon chain can be in either of two orientations. If the hydrogens are on the same side for both sides of the bond, that's the cis orientation, and if they're on opposite sides, that's the trans orientation. Most natural unsaturated fats are cis, so they generally don't get explicitly labelled as cis fats, and just the trans ones get the extra label. Notably, though, vaccenic acid, which is about 4% of the fat in butter, is trans by default, so it's cis-vaccenic acid that gets the extra label.

Unsaturated fats tend to be more liquid at room temperature, but can be made by growing cheap vegetables. They also go off faster as free radicals can attack the double bonds. Saturated fats tend to be solid at room temperature, but mostly need to come from animals or more expensive plants (palm fat is an exception - it's cheap and mostly saturated). It's therefore desirable to use industrial processes to artificially saturate fats, and we can do that by heating them up and exposing them to hydrogen in the presence of a catalyst like Nickel. You don't necessarily want to fully saturate your fat, though, so might stop part way, and if you do, unless you intentionally tweak the process to avoid it because it's the 21st century and you're legally obliged to, you get some of the partially hydrogenated fat switching from cis to trans.

Over the course of the last century, we realised that (except for a few like vaccenic acid) trans fats are harmful in lots of exciting ways, e.g. messing up cholesterol, blocking your arteries, and building up in your brain. They've therefore been banned or restricted to certain percentages in a lot of the world. You can get a similar effect by fully hydrogenating things to get safe (or at least safer) saturated fat and mixing it with the unmodified fat, or by switching everything that used to use hydrogenated vegetable oil to using palm oil, which is one of the driving forces behind turning rainforests into palm plantations.

Apparently, this was twenty five minutes of writing, so I'm nearly up to an hour of thinking about fats.

The Mayo Clinic has a good overview here that explains about the different types of fats

Alton Brown's Good Eats explains fats

https://youtu.be/ukaaesfbO1k

Saturated fats are okay kinda

Trans fats never leave your body. They’re unbelievably delicious but horrid for you.