The problem with travelling to the stars is that they're so far away. To get to even the closest stars in a reasonable amount of time, e.g. a human lifetime, would involve travelling at a significant percentage of the speed of light (186,000 miles/sec). This would require engines based on principles that while feasible, are beyond our technology to build at the present time. However, even if we could build such an engine, there remains the problem of fuel. The faster you want to go, the more fuel you need, which means the mass of the ship goes up, which means more fuel.... but imagine if you didn't need to take the fuel with you.
Interstellar space isn't completely empty - it contains hydrogen atoms, though at very low densities. Suppose there was a way to use that hydrogen as fuel for the engine? Enter the Interstellar ramjet. Ramjets have been used for many years to propel aircraft and missiles to very high speed. The principle is very simple - if you accelerate the vehicle to a high enough speed, it's possible to scoop up air, compress it until it's hot enough to ignite, and it will provide thrust. Very simple, no moving parts and you don't need fuel.
In principle, it was reasoned it should be possible to do the same in interstellar space, where the hydrogen would be scooped and compress to temperatures where it would ignite in a fusion reaction, providing huge amounts of thrust. Several schemes were developed, and it looked like a very promising prospect for reaching the stars.