三 is three horizontal strokes — the tally system, perfected. One, two, three: 一, 二, 三. After three, the lines would get confusing, so 四 and beyond took new shapes. Three is where the simple counting stops.
Three is a powerful number in Chinese thought: 三生万物 ('three gives birth to all things'). It often means 'many' or 'repeatedly': 三思 (think thrice / carefully), 再三 (again and again). The classic 三国 (Three Kingdoms) is one of China's greatest epics.
Three stacked lines = THREE. The tally system at its limit.
三 often means 'many', not literally three: 三思而后行 ('think thrice before acting'). After 三, Chinese stops drawing lines — 四 takes a whole new shape.