Since this is a community based platform, you will probably not get any reply from anyone who actually works at BioWare.
However, I think I can explain a little.
Giving the Multiplayer (MP) DLC away for free is basically just the guys at BioWare being nice to the players, giving some fun new experiences away now and then for the players to enjoy with their friends. Of course this is probably also linked to the fact that if you choose to, you can pay real money to get items in MP, but you really don't have to.
Jaws of Hakkon, the single player DLC on the other hand, is something entirely different. It involves completly new areas, characters and storylines and something that takes this much work just can't be given away for free, especially since the option to possibly make money after giving the content to the players (like with the item system in MP) does not exist with this kind of DLC.
The MP can be accessed via the main menu on PC. It's the third option listed there, after "Continue" and "New Game". It is an online mode in which you can play as Agents of the Inquisition, completing various tasks and defeating enemies on special maps. You can choose to play with friends or strangers in a group of up to four people or even alone.
