No idea how much you know - but here's a very simple introduction to the concept.
In a conventional switching buck (step-down) regulator there are 2 main components. A switch and a filter.
The switch controls the flow of power from the main supply (e.g. 12V) into the filter. The switch usually consists of 2 transistors (MOSFETs) but low-performance regulators may use 1 MOSFET and a diode.
The problem is that the output of the switch is, as you might expect, constantly switching between 0 and 12 V. Pretty much useless for supplying a CPU. The job of the filter is to smooth out these fluctuations. The filter consists of an inductor and a capacitor (or several). When the switch is on, energy is delivered to the CPU, but some is also stored in the filter (the voltage on the capacitor gradually rises, and the current in the inductor gradually rises). When the switch is off, the energy stored in the filter is released to the load (e.g. CPU); the capacitor voltage gradually drops and inductor current gradually drops. This rise and fall of voltage as the switches turn on-and-off is called 'ripple'.
The problem with modern CPUs is that they need huge amounts of current. This means that your switches (MOSFETs) have to be able to handle that current. MOSFETs capable of handling the currents needed are expensive, get very hot, and struggle to switch on and off at the extreme speeds required. The solution is simply to replace 1 switch with 2, or 3 or 4 - and I've even seen one motherbaord with 8. This spreads the current between the different switches. A similar thing goes for the inductors - several smaller ones are often more convenient than one big one.
Now you've got several banks of switches/filters, you could just run them all in sync. But, if you're really clever you can let them run in a staggered (phased) formation. If the individual switches are staggered then at any one time, some will be on, and some will be off. Together, it's customary to refer to a switch and its inductor as 1 phase. Those phases which are on, will be charging their inductors, and those which are off will be discharging the inductors. Because the inductor currents are related to the ripple, different phases charging and discharging will cancel out, leading to drastically reduced overall ripple.
This drastically reduced ripple, gives better power quality than an equivalent power regulator with only a single phase - alternatively, it allows flexibility to downgrade the bulky and expensive filter components (especially the capacitors) without downgrading the power quality.
How many phases you can use depends on the voltage regulator controller chip. Controlling the switch(es) in a voltage regulator can be quite tricky, so specially designed chips are used to do the job. If you want a 4 phase regulator, you need to find a 4-phase regulator control chip.
Information about buck regulators, wikipedia style. I hope you don't have a fear of calculus.
