In more detail
It usually arrives through Phishing attachments, malicious downloads or unpatched vulnerabilities. Ransomware encrypts files and demands payment; a trojan poses as something useful; spyware watches silently. Other families include worms, which spread by themselves across a network, viruses, which attach to other files, rootkits, which hide their presence, and bots, which let an attacker control many machines at once. Good habits: keep systems updated, install software only from trusted sources, keep offline backups and run reputable security software.
Why it matters
The damage ranges from stolen passwords and bank details to locked files, a machine used to attack others, or a company-wide outage. Typical warning signs are unexpected slowness, security software switched off, new browser extensions or programs you did not install, and files renamed or unreadable. Security tools find malware by matching known signatures, such as file hashes, and by watching behaviour; neither is perfect, so a clean scan is not a guarantee, and new or targeted samples can pass unnoticed.
Example
You receive an email with an attachment that Windows shows as invoice.pdf. Its real name is invoice.pdf.exe: by default Windows Explorer hides the extensions of known file types, so only the fake .pdf is visible. The file's first two bytes are MZ, the signature of a Windows program, not %PDF, which gives it away (see Magic bytes). Never open it; check its Hash against a reputation service, or report it. Share any address or hash from it as an Indicator of compromise (IOC).
Common confusion
"Virus" is only one kind of malware, though people use it for all of them. A Zero-day is not a type of malware but an unpatched flaw that malware can exploit.