As you probably know, the power factor is the ratio of the real power to the reactive power. So what does that mean? The real power is self-explanatory. That's the power that gets dissipated doing actual work. The electricity used to light the lights, toast your bread, heat the hot water, etc. It's also the power that is measured by your electric meter (and, therefore, the power you end up paying for).
The reactive power is a different story. It's the power that is temporarily drawn or generated as energy gets stored by or returned from a reactive load (i.e. capacitance or inductance). Reactive loads temporarily store energy during one half of the cycle, then return the energy during the other half. This isn't doing any useful work, and it's not causing the electric meter to spin any faster. In an ideal world, this wouldn't matter. The reactive load is just "borrowing" the energy for a half cycle then returning it to the grid for somebody else to use. However, in the real world, the transmission lines and transformers and switches and generators that make up the power grid all have resistive losses. All that extra current flowing in and out of a reactive load means extra energy is wasted in the grid. It also means that the sizes of all the components of the grid need to be increased to handle the extra current. That's why the power company wants power factors as close to 100% as possible.
If you want a physical analogy to this, think about riding a bicycle from point A to point B, where B is uphill from A. It's hard work to pedal from A to B, not only because you're converting kinetic energy to gravitational potential energy, but also because your bicycle and your body and the interface between the tires and the road and the wind blowing in your face all have significant friction and inefficiency.
Now imagine making the same trip from A to B, except that there are a series of very high and very steep hills in between. Granted, all that gravitation potential energy you build up climbing to the top of each intermediate hill is theoretically returned to you in the form of kinetic energy when you coast back down the other side. In a perfect world, once you reached the top of one hill, you could coast down the other side and up the next hill all the way up to the same altitude you started from. However, if you've ever ridden a bike you know that in the real world that never turns out to be the case. You're usually lucky if you can coast halfway up the next hill. Then it's back to pedaling and huffing and puffing to get up the next one. Even though at the end of the day, you've still only gone from point A to point B, you'll end up wasting a whole lot of extra energy if there are lots of hills along the way. And the worse the power factor is, the taller and steeper those hills become.
Does that make it any clearer?