Many personal finance experts encourage investors to 'diversify' their investments. what does it mean? why is this important? what would be an example of this?

This means that you don't put all your money into one asset. Such a behavior is risky as in such a case you are dependent solely on this single asset. If this one assetdrops in price, your whole investment is affected by this.

Safer strategy is to divide your investment and invest each part in a different asset. It this case if one asset drops, you are safe-guarded by the other assets.

An example would be that you have $1000 to invest. With no diversification you buy one company stock for $1000. If you diversify, you invest e.g. $200 USD in company A stock, another $200 USD into company B stock, another $200 USD into debenture, and remaining $40 USD you put on bank deposit. Of course this is a very simple example, but shows what diversification is.