All electrical loads (including power transmission cabling) are some combination of resistive (R), inductive (L), and capacitive (C) circuits. All AC voltage and current waveforms have some angle between them; the cosine of that angle is called "power factor" and is typically expressed as a per unit (or sometimes percentage) value.
Capacitate load in three phase is used to raise the power factor, since the circuit current in capacitive circuit leads the supply voltage. The measure of the power factor is the reactive power, and the power factor is the cosine of the angle by which the current leads or lags the supply voltage, hence when we raise the power factor, we are actually decreasing the angle of lag between the supply current and voltage, since most loads are inductive, and making the cosine of that angle to be higher i.e. approaching unity, moreover reducing the reactive power, which does no job in a circuit, other than flowing to and fro causing overheating.
Purely resistive loads do not change the AC waveform applied to them at all. This means that voltage and current are running together and one wave shape laid over the other (neglecting amplitudes) will show no differences. Effectively, the "angle" between them is now zero - and the cosine of zero is unity.
Purely inductive loads "slow down" the current. Now the two waveforms are out-of-synch, producing a non-zero angle between them. In fact, the angle is 90 degrees. The term "lagging" is typically applied to loads in this condition because the current waveform "lags" behind the voltage waveform.
Purely capacitive loads "slow down" the voltage. Now the two waveforms are out-of-synch, producing a non-zero angle between them. In fact, the angle is 90 degrees. The term "leading" is typically applied to loads in this condition because the voltage waveform "lags" behind the current waveform. (Also could be stated as "current LEADS voltage".)
Most industrial equipment is primarily a combination of resistive and inductive elements (i.e. a motor). This means that these machines distort the relationship between current and voltage by "slowing down" the current waveform. To counteract this - i.e. bring the relationship closer to identical - capacitive elements are used to "slow down" the voltage and bring the two more in line.
If the angle between voltage and current becomes closer to zero, then the cosine of the angle becomes closer to unity - which means power factor is "improving". Improvement - in this case - means that more of the input power is going toward doing useful work (i.e. producing watts) instead of being wasted (by producing vars).