The father's role at the bris is significant, as he is one of the 3 baalei brit. The blessing he recites is noted as the third bullet-point in the link at the beginning of this paragraph.
While it is uncommon for the father to not be present at the bris, here are a few examples of how it could be that he is not present.
* He is away on business and his wife unexpectedly gave birth early
* He is sick and out of commission
* He has passed away (R"L)
* He is in prison
* He is not Jewish.
