Expressions used in Everyday Spoken English in Social and Professional contexts
To 'put your head down' can mean two things. To literally put your head on a surface in order to rest or to take a nap. You might want to 'put your head down' for an hour if you were feeling sick for example. When you 'put your head down' it can also mean to apply yourself in a determined way to do a task that involves studying, reading or writing. If you 'keep your head down' however, it means to avoid trouble by remaining inconspicuous or by avoiding attention. It can also mean to continue doing something quietly without being noticed by anyone else. These are both idiomatic expressions used largely in social contexts.