Why that sentence is incorrect?....
I think that Esther is only referring to the fact that some plants do like acid soils.
(I'm sure that she can speak for herself - sorry, Esther.
)
To go back to the original question. pH is generally taken to mean 'potential of hydrogen' but there's still some discussion as to what it originally stood for as it is a translation. It refers to the potential of the amount of hydrogen that can be absorbed in water. In plants this is important because it also determines the amount of water and nutrients that it can absorb into itself - very much oversimplified!
Although very important for the plants it isn't something specifically about plants. It's just a method of defining the acidity or alkalinity of any chemical structure. The scale runs from 0 - 14 but there are chemicals that can run off the scale at either end. Also, the pH can be affected (slightly) by the temperature of the water.
The colour of some plants is affected by the pH level and there are quite a lot of plants that prefer slightly acidic soils.
For general gardening the importance isn't particularly high unless you want to grow certain plants. For instance, camellias, azaleas and gardenias prefer an acid soil and will not be able to absorb their nutrients properly in a soil of pH 6.5 or higher. That is why a lot of people, in alkali soil areas, grow them in pots of ericaceous soil.
Funnily enough, there are some plants that help others. Laurel, which prefers acid soils, but is happy in almost any type, will help make the soil around it slightly more acid as the roots spread finely through the soil.
Most garden soils are in the 6.5 - 7 (and almost all are between 6.5 - 7.5) range so are fairly suitable for most plants.
Here's a good link to a list of plants and what types of soil they prefer.
http://lazycompost.com/pH.shtml
Totally non-relevant to the topic but of interest to a lot of people is the pH of hair and skin. These range from 4.5 - 5.5 so are acidic. If you use a detergent shampoo on your hair you will be doing damage to the outer layer cuticle) of the hair because detergents are alkaline. That's why you see advertisements for low pH or acid shampoos (and skin cleansing agents).
To use an analogy, the cuticle of the hair is like fish scales that lie flat on the hair to protect it. If they get raised up then chemicals can enter the hair (that's what happens when colours or perms are put on the hair as they have a high pH level) but the cuticles can then get caught into each other and your hair tangles up.
Conditioners are of a low pH level to try and get the cuticles back down again. Very much oversimplified but it gets the idea across. Try not to use strong detergent or high pH shampoos!
Whoops! That was rather long - my fingers ran away with me!