You can explore once for "free" after your move step, whether you move or not. After that you need to play a card or use a power to explore again.
Actually to be precise, you cannot explore before you take your standard move step (unless you have a card that precisely let you do that... And whether such a card exist is currently discussed).
Then after your move step, whether you decided to move or not, you get one free explore at your now current location if you didn't somehow explore before.
Then after that free explore you can only explore again or move again if a specific power let you do so (power from the scenario, the location, your character or a card you play like blessing or ally are classic examples).
Hoping that clarifies, although I'm never as accurate as Hawk.