Necessary? No. Not much except eating, drinking and breathing is. Even reproduction is optional from the view of a single individual.

A good idea? Absolutely:

1. Exploring space tells us a lot about earth. We currently assume that the moon formed when something big collided with earth and threw lots of material into a stable orbit. This means moon is probably made of the same materials as earth and because there is no erosion nor tectonic activity on the moon, it lets us study what earth may have looked like billions of years ago.
2. Lots and lots of things that were originally developed for space are very useful on earth: teflon coating, memory foam matresses, efficient solar panels and many more. Sure, they could have been developed without space exploration but the pressure to get something exactly right helped a lot. And of course we directly use satellites for a lot of earth stuff, too. Think tv, weather prediction, monitoring of climate change, communication, GPS, accurate maps and many more.
3. It gives humanity something to unite behind. Even during the cold war, the USA and the Soviet Union ignored their feud for a bit to make Apollo-Soyuz happen. These days, the ISS is one of the biggest multinational projects and I dread the day it gets decommissioned because Russia will have one less reason to talk to the rest of the world.