Swaps and options are both financial instruments which are derivative in nature. That is, their value is intrinsically tied to the value of something else. In both cases, they are used by businesses as a form of hedging to minimise the risk or volatility in the expected outcome (e.g. you're willing to give up on potential upside/profit in exchange for reducing the potential downside/losses).
First up, swaps. There are various types of swaps such as interest rate swaps or foreign exchange swaps. Basically these allow you to swap one thing for another. The most common I suppose would be interest rate swap where you can do fixed for floating (also known as variable) or vice versa. Say you have a business loan which is pegged at BBSW + 1% (i.e. the bank bill swap rate + 1%). That means as BBSW moves up/down (i.e. the interest rate; which is somewhat linked to the RBA cash rate), the amount of interest you need to pay on your loan moves up/down. In a worst case scenario, the BBSW rate could skyrocket upwards (e.g. it could move from 3% to 10%) and suddenly your interest payable had tripled! To prevent this sort of thing happening, businesses will do an interest swap whereby instead of having the variable BBSW rate component, they swap it for a fixed rate of say 5%. This way the business knows with 100% certainty for the life of the swap that they will be paying 5% (or 5% + 1% = 6%) interest per annum without any risk of it going up should the interest rates move up. Unfortunately that also means if it goes down, they won't benefit from cheaper interest.
Why would a business do this? It brings certainty and reduces volatility/risk to their profit. If they know they're only going to get $x each year and that amount is fixed, it's in their best interest to try and fix their interest payable so they don't suddenly become at risk of having uncertain profit. There's a lot more to this topic such as the amount of hedging (e.g. not everyone will hedge 100% of the loan), the reasons behind it (e.g. shareholders typically don't like volatile earnings/profit), alternative economic hedges/other hedging instruments (i.e. non standard swaps), pricing of the swap (driven by market expectations on future interest rates), etc... but that's beyond the scope of business studies.
If you are looking at this from an accounting or balance sheet perspective, the gist of it is the value of the hedging instrument (such as the swap contract) should change in value to offset any changes to the interest amount (e.g. if you ended up having to pay an extra $100 in interest (i.e. -$100 to your P&L as it's an expense) as a result of interest rates rising, the value of the hedging instrument also goes up by $100 and hence if you were to liquidate your position or sell that hedging instrument you would receive $100 profit; i.e. the net result of adding the expense and the income will be $nil).
As for option contract, an option is the right but not the obligation to buy/sell something at a set price in the future. If you are a business which relies on buying oil for example (like an airline) then you are at risk of oil prices going up and your profit margins being eroded. Whilst you can change your ticket prices, oil prices change daily and you may have already sold flight tickets to customers and hence you can't control your revenue anymore. Therefore an option contract could be purchased by the airline to lock in the option to buy the oil at a set price in the future. If the oil price rises above the exercise price of the option contract, then the airline can execute their rights under the option and buy it at the agreed price (thus saving them money). If on the other hand the oil price is lower than what the option contract exercise price is, then they can simply not use the option contract. There's other factors to consider in the real world such as European/American options (i.e. when you can exercise) as well as how much the options contract cost (this is driven by market expectations of future prices), but again this is probably outside the scope of business studies.
Hope this helps!