In investing it’s essentially the ability of an asset to change in price rapidly. This doesn’t mean it’s always changing in price necessarily, just that it has the potential to.
Bonds are generally a fixed rate of return paid out at the end of the bond’s term. Their current price is subject to some volatility due to market forces such as interest rates and default risk. They are generally considered less volatile due to the fact that it is uncommon for highly rated bonds to decrease in value quickly, and even in the case of default they generally have high liquidation priority which mitigates losses. They also are generally fixed interest so the price shouldn’t swing too high since the largest possible return is known.
Stocks are generally more volatile since they are subject to pretty much every macroeconomic force you can list. Companies can double in value in a matter of seconds when news is announced, and they can crash just as quickly. Stockholders generally have the lowest liquidation priority which means there is nothing stopping you from losing everything if a company goes belly up.
Options contracts are essentially insurance policies. Depending how you use them they can be a hedge against volatility or a way to leverage it to amplify your gains and losses. You can “amplify” your losses with options since it is possible to lose even more than your investment (which isn’t really an investment since you are paying a premium for the contract, not buying the asset). When this happens it called a margin call and it means you have to settle your balance with the party you entered the contract with.