Active investing is trying to outperform the stock market by picking stocks. You pick stocks that you expect to rise in price, according to various theories of what will affect their value in the future. Warren Buffett is a well known, successful active investor. He identifies the value in stocks before their prices rise.
Passive investing is trying to match the performance of a market, rather than beat it.
Active investors spend time reading financial releases, studying industries, speaking to company management teams, and performing complex calculations to identify stocks they hope will go up.
Passive investors don't study the thousands of companies they could invest in. They also don't trust their gut to help them win the lottery.
They simply hold an index fund, which is a reflection of the economy, and they trust the economy to grow. Passive investing tends to be a far lower cost strategy, in terms of time, labor, and transaction fees, since you can buy one instrument and hold it until you retire.
Trying to find individual stocks that will rise is fraught with risk and extremely time-consuming. Even where some investment firms are able to find stocks that will rise, the rise in those stocks is eaten up by the fees you pay to invest in them. That's one reason why hedge funds usually have returns lower than the whole stock market, which you can own with the push of a button and no study.
The solution is to invest using a portfolio of low-cost exchange-traded funds that broad markets and asset classes like bonds. You can see the portfolio that FutureAdvisor recommends for your individual needs by signing up here.