The way I understand it is that you will get DRM-free copies of the games you have in Steam in your GOG account (provided they are on the list which is expanding over time).
Apparently you have to do it within five days for the games below - if you do the games are in your GOG library forever.
NOTE: You can only connect ONE Steam account to your GOG account, so choose your main one with the most games.
As time of writing the following games are on the list:
Bit Trip Runner
Braid
Breach and Clear
BREACH & CLEAR: DEADLINE
BROKEN SWORD: DIRECTOR'S CUT
FTL: ADVANCED EDITION
GALACTIC CIVILIZATIONS III
MOUNT & BLADE
PROJECT ZOMBOIDIN DEV
SAINTS ROW 2
SHADOWRUN RETURNS
SHERLOCK HOLMES: SECRET OF THE SILVER EARRING
THE INCREDIBLE ADVENTURES OF VAN HELSING: FINAL CUT
WITCHER: ENHANCED EDITION, THE
THE WITNESS
TO THE MOON
TRINE ENCHANTED EDITION
TWO WORLDS
UNREAL GOLD
UNREAL TOURNAMENT GOTY
VVVVVV
XENONAUTS
Here is how it works (from the website):
To connect your library with GOG.com, sign in to your active Steam account via this page. NOTE: Make sure your Steam Privacy Settings & Profile Status are set to public.
You'll be able to permanently import all the games listed below to your GOG.com library – assuming you own them. The eligible games are limited-time offers made possible by participating developers and publishers, so stay tuned for more games to come.
You can connect only one Steam account with your GOG.com library. This process is permanent – choose wisely!
GOG was already my preferred site - now they have been elevated into legendary status!
https://www.gog.com/connect#faq