To beckon is to use a physical gesture to call someone over to you. Universally recognized gestures used to beckon include crooking the finger or nodding the head to invite someone over.
We get the word beckon from the Old English gebecnian, meaning "to make a mute sign," which comes from bēacen, meaning "a sign or beacon." (Remember that "beacon" is a noun while beckon is a verb). When you beckon to someone, you give them a physical sign to "come here." Figuratively, an ice cream sundae might beckon you, calling you away from your diet.