A population can show two types of growth. Exponential growth occurs in ideal conditions when the resources like space and food are unlimited. The population keeps growing exponentially thus showing a J shaped curve. In real life though, logistic growth model is observed. The population starts growing but after it reaches its carrying capacity (maximum number of individuals that can be sustained), it levels off i.e. it stays slightly above or below the carrying capacity, almost like being constant.
Birth rate determines the number of live births per 1000 people in a population. Death rate determines number of deaths per 1000 people in a population. If both of them become equal, it means that there is no effective increase or decrease in population hence zero population growth.