To gain a grasp on options it is essential to understand profit/loss diagrams for the various options whilst also understanding why they display such diagrams. Understanding profit/loss diagrams can help you gain insight into arbitrage trading(which is beyond the scope of this post) and will help you hedge various types of positions. We will first discuss the difference between being long from short, and will conclude why the diagrams are the way they are.
LONG OPTIONS
When you are long an option, you are paying a specified amount of money upfront. What does this mean? This means you can only lose the amount of money that you used to initiate the trade. This is known as having limited loss. Upon paying this premium you have the opportunity to gain infinite profits and will reap such profits if the underlying asset goes in your desired direction, hence you are paying a premium to acquire greater opportunity.
SHORT OPTIONS
Being short options is quite different than being long options. Instead of paying money upfront for the opportunity of large profits, you actually receive money upfront. This is also known as having limited profits. Once you place a short position you already have your max profits set in place. If I receive money upfront then how do I make a profit? Your endeavor as an option seller is for the person on the other side of the trade to be at a loss. Options are a zero-sum game. There are those that profit off of a trader's loss and there are those that acquire that loss. When you are selling an option there is someone on the other side of the trade that is long the option. This is important because as we have learned earlier, long options have infinite profit potential. This means that as an option seller you technically face the probability of having unlimited losses. For example, if you are selling a call there is someone that has purchased the call that you sold. If their call becomes unprofitable then you can buy back the call to offset the call that you have sold, acquiring a net profit. But if their call becomes profitable then you will have to offset the call that you sold, hence buying back the call at a larger price for a net loss.
APPLYING KNOWLEDGE
Lets now take a look at the option's profit/loss diagrams above. The Long Call displays a diagram in which the underlying asset must rise for you to make a profit, with the benefit of having limited losses. The Long Put displays the need for an asset to go down to reap a profit with the added benefit of only having a limited amount that can be lost. The Short Call displays the acquiring of a limited amount of profit with the desire for the underlying to not rise or else an infinite amount of loss will be faced. The Short Put displays the acquiring of a limited amount of profit with the desire for the underlying asset to not go down or else unlimited losses can be faced.
p.s A great way to remember these diagrams is to picture them forming a diamond shape. The image above depicts that of a diamond formation which can help you form new profit/loss diagrams for advanced strategies. It is also very helpful to understand the rights and obligations that the various type of options have.