For example, if you tossed a coin 100 times you would get around 50 heads (and 50 tails). If you did it again you’d still get around 50 heads, but the exact number might be slightly different. If you repeated the experiment very many times you would have a distribution of outcomes: most times the number of heads would be around 50, but you’d have some where you got no heads, some where you got all heads. The actual distribution if you drew a graph of number of heads versus number of times they appeared would resemble the normal distribution: the bell curve. If you then increased the number of coin tosses to, say, 200 and again performed the experiment multiple times you would get a smoother ‘curve’ (the x-axis would go from 0 to 200 instead of 0 to 100). There’s a thing called the central limit theorem that says roughly that if you theoretically increased the number of coin tosses to infinity then the distribution of results would be the bell curve/normal distribution exactly (with appropriate scaling).

It turns out that this normal distribution is very useful for all kinds of statistical analysis, appears quite often in the real world, and has some mathematical properties that make it easy to work with.

The cumulative normal distribution is just a version of the same thing. In our example it is naively a graph got by replacing the actual number of heads on the y-axis of our graph by the sum of all the heads up to that point. That is the value for 2 heads on the x-axis of the cumulative distribution is the sum of the values for 0, 1 and 2 heads on the regular distribution. The real cumulative normal is again continuous and scaled appropriately: it climbs from 0 on the left to 1 on the right. Again this version of the normal distribution is useful in statistics.

See wikipedia for the actual graphs: I don’t think I can post them in a comment.

https://en.wikipedia.org/wiki/Normal_distribution