日 is a picture of the sun. The oldest forms were a circle with a dot in the middle; over time the circle squared off into 日, but the dot (now a line) remains. One sun = one day, so 日 means both 'sun' and 'day'.
日 is everywhere in dates and time: 今日 (today), 明日 (tomorrow), 生日 (birthday). It's also the 'sun' half of 明 (bright) — which you've already learned: sun 日 + moon 月 together make light. Japan is 日本 — 'origin of the sun', the land where the sun rises.
A square sun with a line inside — the SUN, and the DAY it gives us.
日 stacked or beside other characters almost always means sun, time, or brightness: 明 (bright), 时 (time), 早 (early), 晚 (late).