What's the difference between an active investment strategy and a passive investment strategy?

Passive strategy: If you invest $1000 passively, you might put it into an index fund in which the $1000 is allocated to stocks/securities in exactly the same proportions that the security holds in that index. Then the amount of money you earn is proportional to the amount of money earned by all companies in the index collectively. Passive investing is generally considered safer than active investing, because even if one company fails, markets tend to grow overall with time. 
Most people are more familiar with active investment strategies. Active investing means the person managing the portfolio (that is, the investor or someone the investor has hired) may change the proportions based on how they predict a certain company will perform. For example, a lot of people might want to put all of their money into one stock, say, Google or Apple, because they think that stock will perform and take over more of the market, earning them more money. If you single out a particular company and put all your money in their stock, you are actively investing. 
In short, in passive investing, the amount of money you invest will grow at the same rate as the overall market grows because you've proportionally invested in every single company. Active investing means you've singled out companies that you think will perform better than the market and put more money into them. 
Example: 
Let's say in one week, Apple grows by 5% but the overall market grows by 1%. If you passively invested, you earned 1%; if you actively invested all your funds in Apple, you earned 5%. 
However, let's say in one week, Apple loses 5% but the market grows 1%. In this case, if you passively invested, you also gained 1% but if you actively invested exclusively in Apple, you lost 5%. 
Thus, passive investing is safer, but people generally invest actively because they are tempted by the higher earnings potential.