This is the 1468th most frequent Chinese word.
忙
Busy.
Here, '忙' is an adjective meaning 'busy', describing the current state of the speaker.
我最近很忙，没有时间休息。
I have been very busy recently and haven't had time to rest.
In this sentence, '忙' is used as a verb meaning 'to be busy with', paired with '着' suggesting an ongoing action of preparing.
他忙着准备考试，所以没有空参加聚会。
He is busy preparing for the exam, so he doesn't have time to attend the party.
Here, '忙' is used as a verb meaning 'to hurry to', indicating the action of greeting upon seeing the friend.