學而時習之 不亦說乎 it is beginning of Analects. I would translate: to learn and take tome practising is it not said? (spoken)? but it is everywhere translated as pleasant. Why?
說 is the original 悅, they mean the same thing. It's only because in different times, different character may be used to represent the same thing. This situation of different character used is called 古今字. Check this(Chinese Wikipedia).
To back this up, consult (清)段玉裁《說文解字注》
So as to why it's 說, it's because when you explain something (說釋->說明解釋) to someone, he or she will be happy because the you resolve (開解) their question.
Master Sparkles, I don't think call it stand-in word is appropriate since it's just the correct usage at that time. (Sorry I can't comment so I have to reply here)
it's used here as a stand-in for the character 悅, which probably did not exist yet. From the Han Dynasty 說文解字: 說者今之悅字.
Another example of this is 優 as in 學而優則仕: originally 優 was a stand-in for 餘.
說 indeed means 悅 here, but the more puzzling question is why you can use one to stand-in for the other. Almost all true "borrowed characters" (假借字, see list) we know of are "root versions" compared to the eventually created word, which this is not, even though a "兌" could have been possible here.
So the more likely explanation is that they are in fact the same character. But the two phonemes are very different in modern Mandarin, making it difficult to explain how the sound diverged. I've wondered about this problem myself for a while; I eventually found this page (in traditional Chinese) which provided a much more comprehensive argument, and it turns out there is in fact a plausible series of phonological shifts that can explain the divergence (see table in second section).
This theory would corroborate the view that the two meanings actually originated from one character (in pre-Han Chinese), and are not distinct characters. The reason why these meanings overlapped in one character would be hard to discover conclusively, but the one provided by RexYuan certainly sounds plausible.