give the nod
informal verbal phrase

- to give approval, permission, or assent

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A nod of the head is a gesture in which the head is tilted in alternating up and down arcs along the sagittal plane. In many cultures, it is most commonly, but not universally, used to indicate agreement, acceptance, or acknowledgment.

Different cultures assign different meanings to the gesture. Nodding to indicate "yes" is widespread, and appears in a large number of diverse cultural and linguistic groups.
 
Areas in which nodding generally takes this meaning include the Indian subcontinent, the Middle East, Southeast Asia, most of Europe (see below), Latin America and North America. Nodding may also be used as a sign of recognition in some areas, or to show respect. An insult may be inferred if it is not returned in kind.

An early survey of nodding and other gestures was The Expression of the Emotions in Man and Animals, written by Charles Darwin in 1872. Darwin wrote to missionaries in many parts of the world asking for information on local gestures, and concluded that nodding for "yes" was common to many different groups.

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WHY A NOD CAN MEAN YES

There are varying theories as to why nodding is so frequently used to indicate acceptance. One simple theory is that it is a form of bowing, indicating that one is prepared to accept what another person is saying or requesting.

It has also been stated that babies, when hungry, search for milk by moving their heads vertically, but decline milk by turning their head from side to side.

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WHEN YES CAN MEAN NO

Beware, there are some exceptions with some countries swapping the meanings between nodding and shaking head: in Greece, Iran, Lebanon, Syria, Turkey, Egypt, Bulgaria, Albania, and Sicily a single nod of the head up (not down) indicates a "no".

Specifically in Greece, the single nod of the head up that indicates "no" is almost always combined with a simultaneous raise of the eyebrows and most commonly also with a slight (or complete) rolling up of the eyes.

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NOTE

Some other common nods:

to nod off = einnicken
to nod to so. =    jmdm. zunicken
to nod towards so. = mit dem Kopf auf jmdn. deuten
to go to the land of nod = einschlafen

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PRACTICE OWAD IN A CONVERSATION TODAY
Say  something like:

“Management has GIVEN US THE NOD to start the the project.“