The fundamental meaning of becoming is “attractive” but it may refer either to attractive people or attractive behavior (behaviour outside the US), where the meaning leans more toward “appropriate”.
A very comely word, this. The two sonorants, M and NG, help make this authentic English word beautiful. The B and the M are labial sounds, made with the lips alone and their association with affection helps beautify the word. This word originated as the present participle of the verb become but in a quirky meaning that verb bears, “to make attractive,” as in, “That dress becomes you.” You may use this word negatively if you properly prefix it, as in, “behavior unbecoming a gentleman.”
Remember the two senses of this word. It can refer to beauty itself: “Natalie Cladd's broad-brimmed hat sat askew on her hair in a becoming fashion no one could ignore.” As a result, Natalie herself was most likely quite becoming. This word also refers to appropriateness, especially if referring to behavior: “I thought the snippy remark from Maude Lynn Dresser about Natalie's hat was most unbecoming of Maude, though."
The verb become has borne several meanings over its lifetime. In Old English it meant “come to,” which led to the broader sense of the verb today “come to be,” as to become a doctor. The sense of “coming to” also led to the sense of bekommen in German today, “to receive.” Later in Middle English it came to mean “happen to, befall.” The sense of “to befit, to suit” apparently has been expressed as “come to” for a long time in Indo-European languages since idët tebe, literally “it comes to you,” means “it suits you” in Russian.