We need to understand a little bit of how our solar system was formed, and what fate awaits us. The Sun is getting hotter by the day (actually it is getting brighter/hotter at the rate of a 10% increase per 1.1 billion years). If this value is extrapolated, in another billion years the Sun's planetary habitable zone will have moved outward. As of now, Earth is situated towards the inner boundary of the solar system's habitable zone (and Mars just outside the outer boundary). As this shift occurs, the habitable zone will altogether exit Earth. What it means is, the temperature of Earth will have increased tremendously by then! That is, all life on Earth will be gone by then! Ultimately, the Sun will engulf Earth in another 4 billion years (but that does not bother us; we will not even be here much longer than another 400-500 million years).
Now, think about it. We are the only planet that we know of that harbors life. If we are gone, we are gone! People move away from areas prone to quakes, tsunamis; from lack of development and infrastructure etc. Where shall we go when our savior, our creator Sun fries us dry? That means, we need to find an alternate host planet.
Yes, Earth's life must find a habitable host planet.
But how can we do that? By looking for habitable planets. To do that, we need to know the matter-energy dynamics at cosmic scale within our galaxy, to grasp the stellar dynamics and characteristics, to understand planetary behavior, architecture and dynamics. To do that, we need to do a lot of space explorations–not physically travelling in space; we are not there yet! But we need to expand and explore our knowledge and develop tools. What tools?
Our objectives must be (and they are) (1) to understand our galaxy as part of the universe, (2) to define biohabitability of planets, (3) to identify potentially habitable planets, (4) to explore all options and efforts to move to such planets (this includes such technology development we we can possibly be able to distort/mould gravitation and control it for our benefit; very recently it has been mathematically proposed that humans can potentially "create" and control gravitational fields; see [1504.00333] How current loops and solenoids curve space-time).
This (space exploration) is not as simple as Columbus coming to the Americas or Captain Cook landing in Australia (well, those were not simple tasks; but you get what I mean). In a radius of 1000 light years from us, we have not found any sign of life in many planets that we have analyzed so far. That means, a potentially habitable planet must lie farther (and we cannot say how far). To reach the nearest star about 4 light years away, the Voyager 2, which left Earth in 1976, will take 40000 years! That is our snail-esque space-speed. At this rate, we cannot dream of space-faring; remember that our max life span is about 100 years. That means, we need to travel faster. Much, much faster. We also need to travel big! In size! Just 4-5 crew is not enough; the crew must procreate en route and propagate their knowledge and technology over generations if we are to reach an alternate destiny. How much food to take? I wish Roald Dahl actually developed the stuff that he imagined for Wonka's chocolate factory! Besides, forget the worm-whole stuff as shown in Interstellar! A spacecraft will not survive any such phenomenon–let alone dreaming of travelling through it!
We also need to travel safe. To name just a few: first, stellar and interstellar radiations must be negotiated. Second, human development (birth to death life processes) must be studied in details in gravity-free models, such that multi-generational travel could be contemplated. Third, interstellar dust must be negotiated. A 20 micron particle – which we can never see with naked eyes – could cause havoc to the spacecraft.
The other challenge is the communication. Note that Mars is 20 lightminutes away from us. That is, your saying "hello" to Matt Damon on a Martian colony will take 20 minutes to reach him, and when he says "hello" back, it will take 20 munutes more to reach us! So, 40 minutes for a hello-hello combo! That means, we need some other, advanced way to communicate (I am not sure how).
The above are just a few glimpses of challenges we face in order to relocate to an alternate planet. And we must relocate! We barely have a few million years for us–unless our stupid, war-mongering attitude causes a nuclear war and annihilates us before that!
You may say, the Earth will be charred and all lives burnt after hundreds of million years; why should we bother now?
Well, the time we have may actually not be adequate to accomplish the daunting tasks that I wrote above! We must hurry! We have not made baby steps yet!
Hope the questioner now realizes why space exploration is not a waste!