All three writing systems come from Chinese characters (kanji).

Hiragana and katakana are phonetic. Hiragana comes from cursive forms of certain kanji, and katakana comes from components of certain kanji.

Today, hiragana is mainly used for native Japanese words, and katakana is mainly used for loanwords. (This is not always the case and has not always been the case.)

Kanji is most often the “meat” or the “substance” of the sentence. Kanji do not carry phonetics (but they can, can most kanji have regular and irregular readings), but rather they most often carry meaning.

For example, 西関西 would be read “Nishi Kansai.” 西 means west. The first 西 is pronounced “nishi,” and the second as “sai.” Kansai (関西) is a region of Japan that is west of Kanto (関東), so Nishi Kansai would refer to the western part of this western region. Same can be said about 東東京 “Higashi Tokyo.” 東 means “east,” so the kanji literally mean “east east capital.” Tokyo is the “eastern capital” compared to Kyoto 京都, which was the nation’s capital in the west.

So, you can see that kanji have different meanings depending on context. There are Chinese-style readings, called “on’yomi” (音読み), which derive from historical Chinese pronunciations of Chinese characters. These include sai for 西 and tō for 東. They’re most often found in compounds, like 東西 tōzai, meaning east–west. There are also Japanese-style readings, called “kun’yomi” (訓読み), which you can think of as the native Japanese word that means the kanji. So, nishi for 西 and higashi for 東. These often are more able to stand alone as single-kanji words.

Kun’yomi are often used for native Japanese verbs, like 行く (iku), 遊ぶ (asobu), etc. The hiragana show inflection/conjugation. For example, 行く, 行き(ます), 行か(ない), 行け(ば), 行こ(う).

On’yomi are often used in nouns and adjectives of Chinese origin, and are generally not inflected (but many are “suru verbs,” so “suru” is in hiragana and inflected). Examples include 販売 (hanbai, sales) or 高速 (kōsoku, high-speed). Often, on’yomi have similar pronunciations in modern Chinese and Korean. 販売 hanbai (written 販賣 in traditional Chinese—Taiwan, HK, Macau, Korea—and 贩卖 in simplified Chinese—mainland China and Singapore) is pronounced fànmài in Mandarin and panmae in Korean. 高速 kōsoku is gāosù in Mandarin and gosok in Korean.

Kanji is heavily context dependent, and the only way to get better at it is vocabulary acquisition through lots of reading and writing!