What Does the Normalization Factor Mean in the AdaBoost Algorithm?
The normalization factor  is used to reduce any probability function to a probability density function with total probability of one. See Wikipedia.

Say your unnormalized value is [0.1, 0.2, 0.3, 0.2]. You normalize it by dividing it by $z_t=0.1+0.2+0.3+0.2=0.8$, therefore get the normalized value [0.125, 0.25, 0.375, 0.25] which sums up to 1..