Exploration Bonus

Exploration bonus is the second bonus awarded when playing daily challenges: it's similar to the stage bonus but, instead of giving a fixed amount of points for each floor, the player is awarded a precise set of points for exploring and clearing rooms or clearing event flags during his or her run.

Formula
$$ExplorationBonus = RoomBonuses + 100 \times (BossTrapRoomsCleared + 3 \times AngelStatuesFought)$$

As clearly stated above, the Exploration bonus is merely a sum of all the room bonuses accumulated during the run, plus more points awarded for any Boss Challenge Room cleared or Angel statue killed.

Room Bonuses
Each room will have its visited and cleared bonus value assigned according to its type and size, with 2x1 and 2x2 rooms accounting for twice the bonuses for visiting and clearing.

Rooms will default to 10 points for visiting and 40 for clearing if not stated otherwise. 1 Challenge rooms are Mob and Boss-trap rooms 2 It's a 2x2 room, so 10*2 3 If Greed is inside, it's considered a mini-boss room

Boss-Trap Rooms and Angel Statues
As you can see from the formula above, boss (not mob)-trap rooms and Angel Rooms will be used in the final tally of your score. In short, clearing a boss-trap room or killing an Angel statue will yield a lot more points than you previously thought, rendering Angel runs extremely more rewarding from a point standpoint.

Rush and Hush Bonuses
Doing Boss Rush will add 1,000 points; the same goes for Hush, for a total of 2,000 more points.

Enemy Bonus
Killing enemies will also add up to your exploration bonus - roughly 10 points for each killed enemy. The exact formula is:

$$\lceil EnemiesInTheRoom ^ {0.2} \times 5 \rceil$$

So, a room with just 1 enemy is worth 5 points; 2 enemies means 6 points each; 5 enemies 7 points each; 10 enemies 8 points each; 20 enemies 10 points each; 100 enemies 13 points each. Multiple enemy waves in Challenge Rooms and Boss Rush don't yield points, same goes for monsters' spawns (spiders, flies, silkworms, etc).

Strategies
Virtue is in the middle: explore as you see fit to reach Rush/Hush in time, do find Secret and Super Secret Rooms, do fight boss-trap rooms, feel free to skip mob-trap rooms if you're short on time (you "only" lose 200 points), fight Angel statues if given the chance, go into Curse Rooms if you can (no damage penalty, +50 points). If you don't have the Studfinder don't try your hardest to find Crawl Spaces - it will cost you bombs, time and all that for 70 points - go for Secret Rooms instead.