Welcome to Japanese! Japanese is hard! I’ve been working on learning it for two years, ever since I moved to Japan, and there are still lots of things I don’t really understand. However, for the question at hand, I have the answer.
Kanji have two[1] different classes of readings in Japanese. One class is the native reading. This is called kun’yomi (訓読み [くんよみ] in Japanese). When characters occur by themselves, they will usually take kun’yomi readings. Thus in the phrase 犬は木の下に遊んでいます (いぬは きのしたに あそんで います, the dog is playing under the tree), since all of the kanji occur by themselves, we can tell they will take kun’yomi readings.
Some characters also have multiple kun’yomi readings. We can usually (but not quite always) differentiate[2] between kun’yomi readings based on the kana characters associated with them. Thus, for example, we can see three kun’yomi readings for 下 in (1) 下、した、under, (2) 下がる、さがる、to fall, drop, go down and (3) 下さい、ください、please. Because kun’yomi readings are so strongly tied to vocabulary, WaniKani likes to use vocabulary to introduce them.
The second major class of kanji readings is the on’yomi (音読み, [おんよみ] in Japanese). These readings are usually Sinitic, which means they usually come from Chinese roots. Thus, for example, the Chinese word 花 (hua in modern Mandarin) yields the on’yomi ka and ke (か・け). Most kanji only have one on’yomi, which usually reflect Early Middle Chinese pronunciation; there are, however, a few that have multiple on’yomi. This occurs for a couple of reasons. First, the different on’yomi reflect different eras when the word was borrowed–there were historically three major periods of Sinitic borrowing into Japanese. (I think this is behind the on’yomi alternation of にち and じつ for 日.) Second, changes in on’yomi readings can reflect later sound changes in Japanese (男 is consistently read だん word-initially and なん elsewhere, as far as I can tell). Thirdly, on’yomi alternations might reflect either reading variations in Chinese or a Japanese need to add reading variations that did not exist in Chinese (e.g. げつ
and がつ for 月 have noticeably different connotations). Finally, there are lots of places where Japanese euphony yields slight changes in on’yomi readings, usually by rendaku (voicing alternation) or by consonant lengthening, e.g. 日 (にち) + 記 (き) = 日記 (にっき) yields the result nichi + ki = nikki. These changes are fairly regular and, with enough practice, can be readily inferred when encountering a new piece of vocab.
Finally, one last note: While WaniKani usually uses on’yomi for teaching kanji and kun’yomi in the vocabulary, it does not consistently do so. If you are a real stickler for structural consistency, I recommend looking up on’yomi readings for kanji where WaniKani gives kun’yomi readings (such as せん for 川) and manually adding such readings to the list of correct answers, if at all possible.
Hope this helps!
[1] There is a third class, called nanori (名乗り [なのり]), which is used in people’s names.
[2] For example, without further context, 行った can be read as either いった (went) or おこなった (performed, carried out). However, you will not be learning that second reading for some time so don’t worry about it too much.
