The number average molecular weight is a way of determining the molecular weight of a polymer. Polymer molecules, even ones of the same type, come in different sizes (chain lengths, for linear polymers), so we have to take an average of some kind. The number average molecular weight is the common average of the molecular weights of the individual polymers. It is determined by measuring the molecular weight of n polymer molecules, summing the weights, and dividing by n.
The number average molecular weight of a polymer can be determined by osmometry, end-group titration, and colligative properties.