になる (with な-Adjectives), or くなる (with い-Adjectives) is an expression used in Japanese to show that something is ‘becoming (A)’. It can be used with any form of なる, to highlight that something will become (non-past), is becoming (continuous), or has become (past). It can even be used with negative forms, to show that something ‘will not become (A)’.

• 早（はや）く食（た）べて、冷（つめ）たくなるよ。
  Hurry up and eat, it will get cold.
• お茶（ちゃ）が冷（つめ）たくなっているよ。
  The tea got cold.
• コーヒーが温（ぬる）くなった。
  The coffee has become lukewarm.
• 私（わたし）は医者（いしゃ）にならない。
  I won’t become a doctor.

The adjective いい ‘good’ is an exception to the regular conjugation rules for い-Adjectives, and will conjugate as よくなる, not いくなる.

• 勉強（べんきょう）をしているから、頭（あたま）が良（よ）くなる。
  Because I study, I will become smart. (Literally, ‘my head will get good’)