What is bankroll management?
"Bankroll management" (sometimes abbreviated to BRM) is where you play at certain limits to avoid losing all of your bankroll due to bad runs of cards, which any poker player must expect from time to time.
This is called "playing within your bankroll". Subsequently, if you play at higher limits where there is too great a chance of losing all of your poker money, you are "playing out of your bankroll".
Why is bankroll management important?
The reason why you should choose your limits carefully in poker is due to the variance. Variance is a term used to describe the "ups and downs" of poker where you fluctuate from having bad runs of cards to good runs of cards, resulting in varying profits and losses.
If you play poker for long enough there are going to be periods of time where you will consistently lose money, not because you are playing badly, but because the cards are not falling your way. This means that if you do not have enough money in your bankroll to absorb these big downswings, it is likely that you will lose it all.