1) To profit from a market view
Normally, investors only buy stocks to profit from increase in stock price. However, options give you the versatility to profit from any market movement, no matter up or down or even sideways movement.
For example, if you see there will be a rally on the stock price of XYZ company, you may consider buying a call option on XYZ. Conversely, if you think XYZ is going down, you may consider buying a put option on XYZ. If you think the price of XYZ remains stagnant, you may sell a call or put option on XYZ to receive premium.
Please note that the better your prediction on 1) whether the stock goes up or down, 2) how much the price will change, and 3) the time frame it will happen, the higher the chance you will succeed in trading market direction.
2) To hedge underlying stocks against downside
Think of this as buying an insurance policy. You will buy insurance for your house and car, and yourself. Options can be used to insure your stocks against a downturn too. You own a stock and think it has further upside. However you want to limit any losses, you will then buy put option to restrict your downside, while enjoying the full upside in a cost-effective way.