In general when we talk about households we have single phase and three phase.
So basically phase can be explained as the voltage or current between a live wire and a neutal wire.
Now phase is actually the angle which the waveform of the particular value makes. Like in three phase balanced system the three phase waveforms make 120 degree from each other. Also, their is a phase and a angle in the expression of the value like V = 3sin(6t+30°).
Now what phase you want is, if it is a single phase system it will have two wires and if it is a three phase system it will have either 3 or four wires.
Phase means sharing of load if one wire then more load on it and if three wire load will be divided among them. That inturn can be said as 1 ph = less power and 3 ph = more power.