To becalm is to make something quiet, calm, or still. When there's no wind at all on a lake, you can say that the weather becalms your sailboat.
You're most likely to find the verb becalm describing what happens to a sailboat or another vessel with a sail when the air is still and the wind's not blowing. You can also use it to mean "soothe," the way the sound of a familiar voice might becalm a fussy baby. The word dates from about 1550, from be-, "to make," and calm, from the Old French calme, "tranquility."