会 (traditional 會) was a picture of a lid fitting onto a steaming pot — parts coming TOGETHER, an assembly. From 'to gather' it grew two everyday meanings: a 'meeting' (开会 = hold a meeting) and the sense of being ABLE — when skills come together in you, you 'can'.
会 expresses learned ability: 我会说中文 = 'I can speak Chinese' (a skill I gained), versus 能 (physical possibility). It also marks the future/likelihood: 会下雨 = 'it will rain'. And as a noun it's a meeting or gathering: 开会 (have a meeting), 一会儿 (a little while).
Parts coming together under one lid — skills assembling, so you CAN.
我会说中文 — 'I can speak Chinese.' With 会 (can), 说 (speak), and 中文 (Chinese), you can now state a real ability about yourself. That's a milestone sentence.