How does the pH at the equivalence point, as well as the pH range over which the colour of phenolphthalein changes, make it a suitable indicator for titrations between strong acids and strong bases?
If you look at the titration curve, which plots the volume of base added vs pH (source):
you can see that the equivalence point occurs at pH = 7.
Phenolphthalein is fuchsia in pH's roughly between 8.2 and 12, and is colorless below pH 8.2. When the number of moles of added base is equal to the number of moles of added acid (or vice versa; example valid for strong monoprotic acids/bases assuming 100% dissolution), the pH is equal to 7.
You might say, if the pH needed is 7, and phenonphthalein changes at pH's around 8.2, how can you use this indicator?
Well, again looking at the curve, from pH = 11 to about pH = 4, pH changes very rapidly with from an infinitesimally small change in the volume of base added. Since one drop of added titrant will cause this large change, even though the change in color of phenolphthalein does not occur right on the equivalence point, it is within approximately one drop. This kind of uncertainty is "acceptable uncertainty" in using titration to volumetrically determine concentrations.
To clarify what I mean by "acceptable uncertainty", you should realise that each of your measurements has some kind of uncertainty to them:
When you weighed out the primary standard to titrate against, was the balance perfect?
Was your solution made up precisely to the graduation in the volumetric flask?
Did you pipette the exact volume of the aliquot or were you off by a drop or two?
Are you able to state the volume added from the burette to arbitrary precision or is there some uncertainty beyond the two decimal places given by the graduated lines?
In the scheme of things, ~1-2 drops will not be a significant factor in getting an accurate result, but you should most definitely acknowledge that there is uncertainty in your answer.