Kanji have two readings – the on’yomi, which is the original Chinese reading imported along with the kanji, and the kun’yomi, which is the native Japanese reading that already existed before the kanji was applied to it. When Koichi asks for “the reading”, he’s usually after the on’yomi (no idea why).

Typically you’ll use the kun’yomi when a kanji’s sitting on its own or has okurigana on the back (tacked on hiragana used to indicate verb and adjective conjugations) and the on’yomi when it’s in a compound word with other kanji, but that’s only a very rough rule of thumb – there’s about a thousand and one exceptions. You’ll get a feel for it after a while.

The reading he asks for is the most common reading. So when you see the kanji in a word you have a good chance of guessing the right reading. Personally, I prefer to just learn vocabulary instead of kanji reading. Unfortunately the Anki decks provided here are hiragana only so you need to look somewhere else.