Malware, a short form for malicious software, is any software used to disturb computer operation, gather personal information or to gain access to certain content on a said computer. There are a lot of types of malware, the biggest one are: Viruses, Trojans, Rootkits and Backdoors.
It may be stealthy to gather sensitive information, or designed to cause harm, most of all to sabotage.
Viruses are usually hidden within other software and they tend to duplicate them self and breach into other programs or files, and that usually destroys data.
Trojans are, as the name implies, a malicious software disguised as a harmless software. This basically invites the user to run it. After the program is ran, the malicious executable code. The code may affect immediately and can lead to undesirable effects, such as encrypting files or implementing further malicious functionality. In some cases, the user to accept its installation, making the software producer technically not breaching the law.
Rootkits are malicious software that once installed may make other malicious software undetectable and more, some of them defend said software against deletion.
Backdoor is a method of bypassing normal authentication processes, usually over a network connection such as the Internet. Basically, once a system is compromised, backdoors may be installed on other systems on the same network in order to allow access in the future without user` knowledge.
Since the start of 2015, most of malicious software incorporate all of these 4 methods into a big one called Evasion. This basically tries all the method and uses just the one that work.