A trojan is a program that sits and waits for either an event or command or a particular time and or date. So like the Greeks who waited in troy for the trojans to go to sleep after celebating the trojan porgram does the same. It waits for whatever it is programed for and then does its nasty stuff.
What do they do??? Well depends on what one it is and what the programer designed it to do. So could reformat your hard drive (total loss of everything), could low level format a drive (no real recovery, todays drives are a loss, drive replacement), transfer of files and sensitive info to another internet address, moves files, deletes files, renames files (become non accessable by normal program). Could be a simple message one but few of those around as most are designed to be destructive to the user.