Let's suppose that in a few years someone discovers definitive proof that there is life a few thousand light years away.
It will be big news for a week or two. People who are into the idea of ETs will be happy; people who aren't comfortable with them will question (or flat out disbelieve) the evidence. Everyone will discuss the possible implications until they get bored with the topic.
After a month or so, it will fade into the cultural background and life will continue as before. With no way to get there and no means to communicate, the fact of the existence of extra-terrestrial life simply won't have much impact on anyone's day-to-day life.
Net effect on humanity: minimal.