Why does the share market go up in the long run?

It's a cyclic game.

When you see a stock's price move up or down on a chart, that's supply and demand in action. If more people want to buy a stock (demand) than sell it (supply), then the price moves up. Conversely, if more people wanted to sell a stock than buy it, there would be greater supply than demand, and the price would fall. 

Another detailed economic reason:

The government prints money and this money comes into the market. So the peoples have more money than earlier and they start to spend more than earlier.

As people start to spend more so the prices of goods rises. Hence, due to this inflation rises. 

The rate at which inflation rises is on average 6% p.a. so the price of the goods also rises at the level of 6%p.a. Hence, the goods get costlier than the earlier so the profit also increases.

If the people buy more, so the profits of the companies increases. And if the government is increasing the rate at which they print money so people have more and they invest also more.

This cycle of buying more and investing more carries a year after year and hence stock prices increases.

The other reason that companies expand their businesses and generate more revenue and profits so the stock price rises.

Many Stocks rise so the index goes up and up and breaks its new highs.