Why do share prices move up and down?

The answer in two words is 'Demand & Supply'. Simply if there is more demand of a company shares and less people are willing to sell them, the share will move upwards. If there is a huge supply but no body is interested in buying shares at the current price, the share will move downwards.

Now the major question is how does demand or additional supply comes in to the market and the answer is, there are many factors involve in this including company's financial result, overall economy situations, sector performance, government rules & regulations, major political & natural events, future of the company, upcoming products & services, company management changes, stock market frauds  etc.

Any of the above and many more factors affect demand & supply of a company stock and ultimately move it prices to go up & down.

It's very hard to predict stock movement and require lots of research and expertise.