It's where a task is done half-assed without regard for the next person who comes along who is going to be totally screwed. A play on the Pay-It-Forward slogan.
Example: you buy a house and find that the previous owner installed a toilet with no shutoff valve, saving them $2.00 and a little bit of labor, but you come along after the fact and are now totally screwed by their actions if the toilet overflows and you need to shut it off.
You can also be the one to screw it forward. Example, on the last day of your job before quitting, your boss tells you to finish cleaning out some files but you just shove them back into the filing cabinet because you won't be there on Monday. So you smile and tell the boss "OK, sure" but you say to yourself, "yeah whatever...well I'm not going to be here anymore, so I'm just gonna SCREW IT FORWARD to the next person and they can deal with it...cuz I'm outta here!"
(Can also say fuck it forward or fucked it forward, as in: "Those guys fucked it forward pretty bad for the rest of us who have to clean up this mess...").