Related What are the factors that contribute to the stock prices that go up and down every second?

Think of the stock market as a massive treasure hunt, where we all collectively look for clues to win millions of independent treasures all the time. We might look at both the logical clues as well as follow the members of opposing teams. Some of these clues are only remotely relevant to the treasure we are searching, but we still take it.

Information

Every minute there are 100s of new news items emerging from different corners of the world. Some of the news items:

1. Announcements of Central banks & Governments (such as US Fed, ECB, BoJ): When government makes a big decision, everyone takes a notice. They change interest rates, can move the currency or change policies. Market reacts the most to these. There are dozens of important governments and central banks & they make periodic releases.
   
2. Periodic economic data releases: Various agencies release data that gives a clue of how a particular economy is doing. Some of the most watched data include those from US Bureau of labor statistics. If US unemployment Everyday dozens of these stat release happen all over the world.
   
3. Wars & Conflicts: Nigerian terrorists might blow up an oil field. Iranian mullahs might issue a new Fatwa. Syria might threaten to gas up some more people. All of these can change both supply and demand of essential items like oil. When oil prices change, everything else would change in a progressive manner.
   
4. Earnings data from companies: When Apple releases its earnings, it gives investors clues about other tech and consumer companies. Then investors go on to buy or sell the other stocks.
   

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Many of these news items take hours or even days to propagate around the system. Think of information propagation like creating a vibration on a metal. The metal would continue to oscillate for a while after the impact, but with a dampening factor. Each of these information sources propagate through the market like this:

The stocks related to the information will move a lot right after the release and then the effect of that information on the stock movement will start to damp. Then after a while, some other information comes. This is one of the key items you see in the stock price.

Psychology

Investors have their own personal factors. If you plot your most upvoted answer on a graph (with the y axis being the number of upvotes you got everyday) you could see that there are both random & psychological factors. The market works quite similarly.

1. Bandwagon effect: Joshua Engel has upvoted this and so this must be a good one in science. Oliver Emberton has written this and so this must be a good one for personality development. In the same way, market looks for various leading traders and then pile on those stocks.
2. Calendar effect: Investors typically sell their stocks before holidays or tax season, and then buy it after they return from vacation. Thus, January will move the stocks up and December will move stocks down. While these investors buy/sell these stocks, others will try to use this fact and make some short term money.
   
3. Personal issues: People might sell a big chunk of their stocks due to life events. A family controlled business might have one of the key persons looking to get out of the stock for paying off the gambling debt. This could move that stock.
   
4. Weather: A gloomy weather or a storm could affect the market in various ways. Traders are humans, after all.
   

Rumors (Information + Psychology)

At any point of time the market is filled with 1000s of rumors -"CEO x is sick, Fed is going to increase rates, Bernanke will be out of Fed in 6 months, President of X nation is dying, sales of product y is not good....".

The credibility of these rumors goes up and down over time. There are a lot of random factors at play too. These rumors will keep the stocks oscillating. There are also a few self fulfilling prophesies.

Trading Artifacts

Traders in big institutions use a number of automated trading systems. These systems constantly react to movement in the market. Both by design and through buggy implementations, these systems introduce a lot of randomness into the market.

When a bunch of poorly designed algorithms compete with real money, there will be volatility.

Ultimately don't discount the random factors. A lot of what is going around us is random and we are constantly fooled by the randomness by reading too much into these patterns.