Let us start by sorting out a few definitions:
Equivalence point: this is when exactly equal stoichiometric quantities of acid and base have been mixed and reacted together.
Endpoint: this refers to the situation where the indicator changes colour.
Now consider what happens with four different combinations of acid/ base titrations:
Phenolphthalein is going to be used as the indicator - this indicator is accepted to change colour at pH 8.3 - If added to an acid solution, it is colourless, and when a base is added, when the pH reaches 8.3, it starts to go pink.
1) strong acid / strong base: titrating 25.00mL of 0.100M HCl with 0.100M NaOH
Equation: HCl + NaOH → NaCl + H2O.
Here the product NaCl is neutral, and the equivalence point will be at pH = 7.00 when exactly 25.00mL of the NaOH solution has been added.
But because the base is strong, during the titration, the pH of the solution will be found to change from the acid pH approx 4.0 to basic pH 9.0 by the addition of 1 drop of NaOH solution. This range spans the endpoint of the phenolphthalein indicator, and as a result it is a suitable indicator for this titration.
2) Strong acid/weak base. Titrating 25.00mL of 0.100M HCl with 0.100M NH3
Equation: HCl + NH3 → NH4Cl
Here the product NH4Cl is an acidic salt and the equivalence point will be at an acid pH - probably around pH = 4.5. This will be attained when exactly 25.00mL of the 0.100M NH3 has been added to the 25.00mL of 0.100M HCl. In order to bring the pH up to the phenolphthalein endpoint, pH = 8.3, considerable extra NH3 solution must be added . Remember NH3 is a weak base, and it takes quite a high concentration of base to increase the pH from about 4.5 to 8.3. So in this case phenolphthalein is an unsuitable indicator for this type of titration - its endpoint does not match the equivalence point of the titration.
3) Strong base/ weak acid. Using the same argument as above - titrating a weak acid- CH3COOH with a strong base NaOH - the salt is CH3COONa - which is basic, so the equivalence point is at pH well above 7.00 Here a drop of the NaOH solution will change the pH of the titration solution from acidic to pH approx. 9.0 . Again this rapid and instantaneous pH change spans the endpoint pH of the phenolphthalein indicator - it is therefore a suitable indicator for this titration.
4) weak base / weak acid. Here the salt is neutral - consider CH3COOH + NH3 → CH3COONH4. The equivalence point occurs at pH = 7.00 - well below the endpoint pH of the phenolphthalein indicator. But because both acid and base are weak, the change in pH throughout the titration occur very slowly. In general this type of titration is considered by chemists to be avoided if possible - and no indicator is really suitable - definitely not phenolphthalein.
So there is your answer: phenolphthalein
1) suitable for strong acid / strong base: weak acid / strong base
2) unsuitable for weak base / strong acid or weak base / weak acid.