Explore Nodes are available in the single player campaign. As part of the story line, each plane (Innistrad, Theros, Ravnica, Shandilar, and Zendikar) has story related duels that you must win to progress to the next plane. For this achievement, you must win five "Explore" duels in each plane. You will receive a booster pack with cards from that plane for winning each of these duels.
Note: You must beat Avacyn, the final story related duel in Innistrad, before Explore Nodes become available.
There is no way to track your specific progress towards this achievement, but you can look at your stats in your Player Profile to see how many planes you have "fully explored." Winning five "Explore" duels in a specific plane counts as fully exploring that plane, so I suggest focusing on one plane at a time before moving on to the next.
Also, in order to unlock all of the cards for the collection, you will end up playing many more than five "Explore" duels in each plane.