The short answer to your question is that the part that isn't listed as saturated or trans-fat is either mono or poly. You can't really generalize by saying mono or poly is better than the other. Your diet will need some of each.
The long, geeky answer is:
Fats are categorized by the number of double carbon bonds in a fatty acid chain. If there are none, it is saturated, because no more hydrogen atoms will fit on that chain. If there are double bonds, that fat is unsaturated, because a double carbon-carbon bond can become a single carbon-carbon bond by allowing two more hydrogen atoms to join the party. If a fatty acid chain is monounsaturated, that means there is one double bond, and if it is polyunsaturated, it has two or more double bonds.
Unsaturated fats tend to be liquid at room temperature as opposed to saturated fats, which tend to be solid. You can't pour butter, lard, or coconut oil at room temperature like you can olive oil or canola oil. The reason for this is because unsaturated fats, because of their double bonds, are bent and don't stack together nicely. Think of a bunch of branches with bends in them. They don't stack nicely compared to straight logs, and it would be harder to tie them all together into one nice group. The same is true of unsaturated fats. They don't clump together like butter does within its wrapper (or your arteries).
Most unsaturated fats are good for you. Monounsaturated fats, such as oleic acid, are found in things like extra virgin olive oil, avocado, almonds, and cashews. You can get too much fat, even good fat, but you should be getting a decent amount of monounsaturated in your diet.
Polyunsaturated fats are a bit more complicated. The two most often mentioned groups of PU fats are omega-3's and omega-6's. Omega-3's are found in walnuts and flaxseed as something called ALA and in certain fish, e.g., salmon, as DHA and EPA. ALA is healthy but the body ultimately needs DHA and EPA and isn't too great at converting ALA to them. Omega-3's health benefits are maybe sometimes overestimated, but there's no doubt omega-3's can make a huge difference in one's health. Omega-6's, like omega-3, are also necessary for good health and, like omega-3, can't be made by the body. (In other words, omega-3 and omega-6 are both essential fatty acids.) But almost everyone gets too much omega-6, and the ratio between omega-3 and omega-6 is too low for almost everyone. So, there's no need to go looking for more omega-6.
One bad thing about unsaturated fats, esp. polyunsaturated, is that they are less stable than saturated fats and more likely to become rancid (i.e., chemically change into something that tastes bad, smells bad, and is bad for your health) than saturated fats. Therefore, keep them away from high heat as much as possible. For instance, don't bake or cook with olive oil, but put it on after your meal is already cooked, or put it into a salad. Also, don't overcook salmon---that destroys omega-3. Healthy fats, as much as possible, should be kept in the dark and used somewhat quickly.
Trans-fat is technically an unsaturated fat but it shares none of the health benefits of them. A trans-fatty acid has a double bond that, has an S-shape rather than an L shape like a natural and healthy unsaturated fat. In other words, it bends a tiny bit and then it bends right back in the same original direction. Therefore, trans-fat stacks together nicely and stays solid (as shortening does), making for a long shelf-life and giving certain fried items a crunchy sort of taste. But unlike saturated fat, it's totally unnatural. Your body really doesn't know what to do with it except let it make you fat and block your arteries. Your body needs some saturated fat, but trans-fat is totally harmful.
Food labels must say how much fat is in a serving, as well as how saturated fat is in a serving. More recently, the FDA required labels to reveal how much trans-fat is in a serving. However, they aren't required to say a product has trans-fat in it so long as it is no more than 0.4 g more serving. So, if the servings are small and you eat several servings, you could be consuming quite a bit of trans-fat from "trans-fat free" foods. IMHO, avoid foods with hydrogenated oil in the ingredients list. Try to get your fats from fish (and not deep-fried, either), grains, nuts, avocado, and extra virgin olive oil.
