Some dice have abilities on them that when rolled, are activated Immediately. As you can see in the picture (I'm going to update the picture later so no complaints yet haha), there are a few different symbols signifying an Immediate Effect.
One of these symbols is the reroll symbol, which appears as two curved arrows pointed at each other. This indicates that you will Immediately reroll that die, and possibly another die if indicated by the card's ability. For example, one of the faces of the Assistant has a reroll with a burst. When rolled, you reroll the Assistant die and another die of your choice.
The second symbol is a spiral with a number in the middle. This indicates using the Immediate Portal abiliity. The Portal dice aren't the only ones with the ability, however. Some creatures have this as an added effect as well.
Last, but not least, is the Burst symbol, which can be an Immediate effect, if stated on the card. These can have a variety of effects depending on the card.
For a full reference to dice with Immediate Effects, check out the Imm Eff FAQ.