An idiom is a type of phrase or expression that has a meaning that can't be deciphered by defining the individual words.
engage in (something)
to be busy with something, to be occupied with something
The man is engaged in a new project. The woman was engaged in a long conversation.
List of common idioms, their meanings and examples of their usage in sentences
Idioms can be a powerful linguistic tool only when they are used in the right way in the right places.