Final answer:
The word 'beckon' means to signal or summon someone using a non-verbal gesture, often in a way to attract their attention or prompt them to approach.
Step-by-step explanation:
Based on the context clues provided in the sentences, the word “beckon” means to signal or summon someone using a gesture. In the example sentence, “Hungry and impatient, she beckoned the waiter,” the context suggests that she made some sort of gesture to get the waiter's attention. Moreover, the additional examples imply situations where a person is prompted to come closer or to do something in response to a non-verbal cue, indicating that beckoning is a silent form of communication that involves gestures, as opposed to verbal commands.