The rocket equation is a harsh mistress, it demands exponential amounts of fuel the faster you want to accelerate a given stage (specifically, as a ratio to the exhaust velocity of the rocket). Given that orbital velocity is quite high (about 8.5 km/s) relative to the exhaust velocity of the best chemical propellants (about 3 km/s for LOX/Kerosene) this results in impractical mass fractions to contend with (17:1 to get to orbit, and that's with no payload). But you can cheat. If you use staging and drop away the dead weight of empty fuel tanks and no longer needed engines from lower stages then you can make an end run around the rocket equation. You make a rocket that can accelerate a payload up to a certain velocity, then you make an even bigger rocket which can deliver the entire other rocket as a payload to a different velocity, and so on, until the sum total of all the velocities is the necessary total speed you require to get to orbit.

We're actually fairly close to being able to make single-stage-to-orbit (or SSTO) launchers workable, but it's a difficult problem. We can just about make a single stage with a high enough mass fraction to do it, but then there is almost no payload remaining. And the only way to make a vehicle with such a tiny payload cost effective would be to make it reusable, but enabling reusability would add additional weight which would destroy any payload whatsoever and probably prevent it from even reaching orbit, catch-22. Potentially we could use advanced engines, rocket fuels, and lightweight materials (like carbon fiber) to build a reusable SSTO which would have a reasonable payload, but such designs are hugely untested and very risky. So for now the best hope for reusability seems to be to incrementally advance the design of existing multi-stage rockets.