Mill accepted Bentham's idea that the greatest happiness principle is the basic statement of moral value:

" Actions are right in proportion as they tend to promote happiness, wrong as they tend to produce the reverse of happiness. By happiness is intended pleasure, and the absence of pain; by unhappiness, pain, and the privation of pleasure." (Utilitarianism 2)

But he did not agree that all differences among pleasures can be quantified. On Mill's view, some kinds of pleasure experienced by human beings also differ from each other in qualitative ways (meaning one sort is better than the other, and more desirable.Mill identifies higher pleasures as those which people "would not resign for any quantity of a lower pleasure (Utilitarianism (II, 5).

Mill's describes the difference between higher and lower pleasures as a difference "in kind" that assumes "that character of absoluteness, that apparent infinity, and incommensurability with all other considerations" (II, 8), (V, 25).  For example, listening to Mozart is superior to rap music, and music is superior to computer gaming, and only those who have experienced pleasure of both sorts can judge their relative quality. This establishes the moral worth of promoting higher (largely intellectual) pleasures even when their momentary intensity may be less than that of alternative lower (largely bodily) pleasures. He concludes that it's "better to be Socrates dissatisfed than a fool satisfied".

It is better to see Milll's "higher pleasures" as "higher sources of pleasure", where the source is a means to a state of being which itself can be subject to evaluation.  For example, taking drugs could be seen as "bad" not just as a source, of pleasure, as it destroys health, but also as an end, because the pleasure it gives is transitory and addictive, and liable to good and bad elements of experience.  So we can talk about "good pleasure and "bad pleasure".  It's more than a description of a state.  It's an evaluation of that state.

Even so, Mill granted that the positive achievement of happiness is often difficult, so that we are often justified morally in seeking primarily to reduce the total amount of pain experienced by sentient beings affected by our actions. Pain—or even the sacrifice of pleasure—is warranted on Mill's view only when it results directly in the greater good of all.

For a detailed article analysing Mill's division fo lower and higher pleasures click here.

For a discussion of whether Mill is asking us to rank pleasures or providing an argument for a higher capacity for pleasure, click here.