In Lesson 21 you learned the Vたい form, which express the speaker's own desire, "I want to..." At the same time, you were cautioned not use the Vたい form to express other's desires. The others' desires are expressed with the prhase Vたがっている. This form literally means "show the sign of wanting." The implication here is that one cannot know what others want directly, but only indirectly by inferring, through hearsay, or by observing... As you may guess, the difference between Vたい and Vたがっている is closely related to the difference between と思う and と思っている. As seen in both cases, the Japanese language is more sensitive to the distinction between speaker's own private world vs. others' worlds than English is.