You hear this term "Next Man Up" in society in different ways:
1. In sports, its when an ineffective player or injured player is sat down, it becomes about the Next Man Up
2. In church, they talk about boys and immature guys stepping up and being the Next Man Up
With our song, we are using the thread/angle of the woman character has kind of had enough with hi-tech dating services and just wants the Next Man Up to be "real".