なる means 'to become' and is used to describe a change into a new state. When something changes into a noun or a な-adjective, you mark the new state with に. For example, if you become a teacher, you say 先生になる. If the weather becomes quiet, you say 静かになる. For い-adjectives, the ending changes: い becomes く, then add なる. So 安い (cheap) becomes 安くなる (become cheap). For verbs, use the dictionary form plus ようになる to express that a situation changes so that something happens, like learning to speak Japanese: 日本語を話すようになる. This is a common pattern in everyday conversation, but it is not too casual; it can be used in both speech and writing.