The three-phase system provides three conductors, which have 120° out of phase voltage applied. So, if we consider phase A (say Red) to have the reference voltage on it (measured with respect to neutral for this description) then that voltage will climb to a maximum, drop down through zero and to a negative maximum, and then climb back up to maximum again, fifty times a second (or 60 in the USA et al).
The second phase B (say Blue) also has the same voltage, but it is delayed 120° in phase. This means that there is a voltage between Red and Blue that goes up to a maximum, down through zero, to maximum negative, then back up to maximum again, according to where in the cycle we are at any given time.
Sometimes the Red phase and blue phase will have the same voltage across them, for an instant, as Red is dropping, and Blue is rising.
The third phase C (say White) has its phase delayed by 240° from Red. So, there is a voltage between all three conductors, which changes throughout the cycle. So, for a load (say a three-phase water heater), the three phases can provide a voltage difference between them, providing energy to heat the water. At some points in the cycle, the current is flowing out of Red and into Blue while White is at zero. At other points, current flows out of Blue and into White, while Red is zero. At other points again, White sources current which flows into Red and Blue.
In this scenario, a neutral connection is not required for the transmission of power, as the three phases source and sink current according to where they are in the cycle. A ground wire would be required for regulatory purposes (i.e. safety). But not for energy transmission.