If you delete files from Dropbox, the files will also be deleted from the servers. This is if you right-click>Delete, so in simple terms the servers will receive an 'instruction' to also delete the files there.
Delete files as you normally would on computers, phones, and tablets, and they'll be deleted from the Dropbox website, too. You can also delete files from the Dropbox website, and they'll be removed from all the computers, phones, and tablets attached to your Dropbox account.
If your PC crashed, the files would still be online as the servers didn't receive the 'instruction'. Most likely result would be the files would be downloaded again from the cloud should you install and sign in to Dropbox on a new PC. Don't worry :)
By the way, if you delete files from Dropbox, you are still able to restore it within 30 days as Dropbox saves a history of all deleted and earlier versions of files for 30 days for all Dropbox accounts. (That is, unless you clicked Pemanently Delete instead of normal Delete).