When you defeat a creature within a dungeon, or receive a reward for healing, you will be forwarded to the "Player>Rewards>Pending" page and given a Dungeon Reward.
All dungeon rewards are either improved or made more frequent by the Consecutive Wins counter. Here are specifics:
With the exception of skill items, the only way to increase the frequency of a reward dropping in a dungeon is with a Dungeon Bonus Item. Without a Dungeon Bonus Item, dungeon rewards have the following set drop percentages:
Under the "Dungeon Bonus Item" menu you can select a Dungeon Bonus Item you possess to increase the drop percentage of a particular type of reward.
Please note that Dungeon Bonus Items last only until at least 30 minutes have passed since their activation or you use the Reset Floor button in a dungeon.
Please note that you will not see this menu unless you have a Dungeon Bonus Item in your inventory.
Should you run out of inventory space for equipment, creatures, marbles etc., this screen will allow you to either sell them for coins or make room in your inventory so you can receive them.
On the other hand, if you did have enough space, the reward will be automatically given to you and you can continue on through the dungeon.
When you are done making space for your reward, you can return to it with the "Player>Rewards>Pending" link to claim it.
Please note that your pending rewards are erased as soon as you enter another battle. However, pending rewards given to you by quests will still be available to you until the first of the next month.
Naturally, this means gaining Consecutive Wins in more difficult dungeons on the Daisy Pusher difficulty setting will net you far greater rewards.