The Earth spins around itself once every twenty-four hours, like a top spinning on its axis. The side of Earth facing the sun at that moment has bright daytime, while the opposite side, which gets no sunlight, has dark nighttime.
Because the Earth keeps spinning without stopping, every place on Earth takes turns having day and then night. This also explains why time differs between countries: while the sun is rising in one country, night may have already fallen in another, far away.
The sun itself does not move around us — we spin around ourselves while also traveling around it, just like a child spinning in place while walking in a big circle around a tree.