To learn 闹, it’s better to know the meaning of 市 first. You can see 闹 is composed of 门 door and 市 market. A market is a noisy place, so the original meaning of 闹 was noisy, which is very well expressed by the phrase, 闹市 noisy market.
In Chinese, many adjectives can be turned into verbs which have meanings related to these adjectives, e.g. 闹. The meaning of 闹 is extended from noisy to noisy-related verbs such as make a noise 吵闹, celebrate 闹元宵, suffer from 闹水灾, etc.