Basically what that means is that when your character moves or when an enemy moves, they will move in their specified direction by a number of pixels until they've reached the next tile, then they'll stop. Detecting when two movers have bumped into each other will, instead of being done on a tile-by-tile basis, instead be done with collision detection where if one mover is within a certain distance in pixels to another, they've bumped.
What that means is that you, as the player, won't be harmed by enemies until you're actually close to them in terms of pixels. So if you're moving onto a tile that the enemy is moving off of at the same rate, you'll never touch. Likewise, if you see an enemy moving onto your tile, you have a brief moment to start moving your character away from that tile before the enemy will harm you.
Hopefully those changes will remove some of the frustrations from the older system - the difficulty of trying to figure out which way enemies are moving.
I was thinking I'd give the game an over world map, which is just a quick way for the player to wander around the world without having to explore a bunch of empty terrain. On the over world map there would be villages made up of individual houses that the player can enter for a zoomed in view, and dungeons, which are places that the player can enter in search of loot.

Westrose Island, a possible overworld map.
Loot is the main reason for the player to enter dangerous areas now. Finding treasures will get you money, and money will get you where you want to go. You may need to pay for passage through a mountain pass, or pay a fee to cross a span of water on a ferry. Of course, you'll need to buy some equipment in the towns, too. But for the most, towns will be there as a place for the player to glean information on where to find things, and just to give the game a general feeling of not being so alone.
I'm thinking I'll throw in a nice little fade in, fade out visual effect for when the player enters a house or dungeon, or changes rooms within the dungeon. So when the player goes through a door, you'll see the door open, a glimpse of what's on the other side, then everything will fade out, then fade back in again with the player on the other side, then the door closes. This will help to differentiate areas, so that its easier for the player to know when an area has been reset.
I still need to figure out a good overall goal for the story though. Anyone have any suggestions? I was thinking either a "find your missing friend" or "find the legendary treasure" type of quest. So you'll find yourself on an island, hunting for treasures in order to pay your way and find the items that you'll need in order to get to your primary goal.
If you come up with an element theme, that could help. Example. Boss bad guy dammed all the water which dried up the rivers which is hurting town folk. The people in the town drew straws and the player is the unlucky one to go fix the problem. Proceed to dangerous terrain and adventure. The theme is water. A lot of puzzles involve letting water flow at the right times to unlock, float, flood, move the player, and etc. It's endless fun. A few major milestones can be unlocking (each dam has a new challenge to unlock) the dams to let a little water flow through. Cheers are heard from the local town. The more dams which are opened, the farther the water travels down the snake river. An overview map can show how far the river is reaching. Since the players town is last, the water will on reach his town via the snaky river after beating the final boss and releasing the largest dam.
To beat the boss (Spoiler)... heh.. you flood his chamber and send him down the river with all the water and out to see. Pan to the overview map where you see his icon floating down the river and out to sea where he is eaten by a large serpent. lol.. ok im done.