Definition of bankroll
A poker player's bankroll is the money he or she spends on poker. What is meant by a bankroll is like a bank account, but specifically for poker. Depending on how serious a player is, his bankroll will vary. If you are a beginner and want to get started in the world of online poker, perhaps you will deposit 100 Euros at an online poker room. If you grow your bankroll, great, if not, maybe you'll retire. Your $100 will be what we call your bankroll.
Bankroll management
Bankroll management is a very important aspect for all poker players. Your bankroll will determine the limits at which you can play (as well as your skills). With a bankroll of $100, probably $5 buy-in cash game tables would be appropriate for you. If you are very skilled, perhaps more aggressive bankroll management might be an option, but be aware that there is still the risk of losing your entire bankroll. If depositing for you and dipping into your "regular money" to invest in your "poker bankroll" is not a problem, it might be worth considering. For tournaments, it is suggested that you invest no more than 1% of your bankroll in each tournament you play.