Can a pdf file really damage my computer?

If it really is a .pdf and not some executable that just has .pdf in the name to trick people, no.

Yes. There are a number of known vulnerabilities in adobe reader that malware can take advantage of. This is why adobe keeps releasing security updates to patch them. Word files can also host malware and but it’s not as common as it used to be.

Ransomware/Malware such as Cryptolocker is disguised to look like a .PDF file. Once launched it executes encryption that locks your files. The encryption key then needs to be purchased from the Ransomware owner in order for you to get access to your files. Don’t open attachments that look suspicious or are from people you don’t know or trust.
http://en.wikipedia.org/wiki/CryptoLocker

@Lightlyseared , So that’s why they have all those updates. It makes sense now.

Foxit Reader is a bit more secure, as it has different holes (and probably fewer of them). It’s not totally immune, but a bit more secure.

Word documents can, mostly through the use of macros, but as @Lightlyseared points out, that is less common than it used to be back in the day. In fact, pretty much any file can, but the most common in my experience are archives (ZIP, RAR, 7z….).

@BosM Ahhhh ransomware. Nothin like turning on your computer one day to see “YOU HAVE BEEN CAUGHT LOOKING AT CHILD PORNOGRAPHY!!! PLEASE SEND (LARGE SUM OF MONEY) TO FBI AT (RANDOM ADDRESS) SO THAT CHARGES AREN’T FILED.”

Sometimes PDF files have naughty bits attached to them.

Cryptolocker is actually very easy to deal with if you keep your files backed up. So there’s another reason to back stuff up.