The 'birds-and the-bees lecture' is when a parent tells their son or daughter about love and sex and where babies come from!! The parent is often very embarrassed to talk about it, and behaves like he is saying something very important and serious. The sentence means that the man spoke in a manner that was quite awkward, filled with reluctance and embarrassment.

A lot of schools cover this topic now in their Health Education classes.

Neal's answer is good. Part of the reason that the parent is not comfortable is they are wondering all the time how much their kid already knows.

"The birds and the bees" is an idiom for sex. It would most likely mean that he spoke in a reprimanding tone.