A computer virus is so named because it mimics a virus in the human body. It will attach itself to a piece of programming and rewrite that program so it turns out more copies of the virus which then attach to other programs and etc. Viruses are not as common now since modern technology has given us new tools. The only real exception is the polymorphic virus which can change what it looks like and so hide, for a time, from computer anti-bodies.
In ancient Greece a bunch of soldiers crammed themselves into an incredibly tight hollow wooden horse. The horse was supposed to be a tribute to the Troyan Armies and they allowed the horse to be brought into the city. After everyone in town had passed out the soldiers came out of the horse and.... well you know the end. A Trojan on a computer is no different. It would look like anything but a malicious piece of code. Rather it might be a photo, a video, or even an advertisement. You download the photo or whatever and when you open it the Trojan is released. Trojan damage is severe and fairly commonplace. Luckily it is also VERY recognizeable by anti-malware programs.
Ransomware is just what the name implies. A nefarious person manages to lock your computer and it won't start again. Usually there is also a veiled threat associated with the malware. Our example here is that the FBI has locked the computer due to suspicion of illegal conmtent. Bet on one thing when it comes to the Beureau. If they have suspicion that there is something illegal about you, in or out of your computer, they will come to your door with a warrant in their hands.
Addware is rarely dangerous but it can be annoying. It comes in an unbelievable number of flavors too. Before we go any farther addvertisements are what drive most websites today and not so much what they are selling. In the confusion crooks appear. The major adware type involves annoying pop ups that offer a great deal. Only it either isn't a great deal or it isn't worth the price. Addware also sets up when you accept cookies from a website and don't purge them from your browser on exiting. This can also slow your browsing down.