Every person who wants fresh new coins to play our game needs to mine for them. If you don’t want to or can’t mine, you can of course, get them from someone else. But eventually up the chain someone mined those coins in the first place. Mining is the only mechanism to get new coins into the game.
For mining to work, we need a difficult problem for computers to solve that can be reused, otherwise we could only only create coins one time at the beginning of the game and that’d be it. That would mean that the first person to play the game would get all the coins for themselves, and nobody would want to play afterwards.
That problem to be solved in Monero is to take a huge number and find a number that divided by it, gives a result with many zeros at the end. The most important thing about this problem, is that it cannot be automatically calculated by a formula, the computer has to try every number until it sees one that works.
In practice, it’s like lottery tickets. You cannot guess in advance which number is the winner, theoretically they all have the same chance of winning. However, what you can do to increase your chances is buying more tickets. In the case of proof-of-work, it would mean using more computers to mine, mining with more powerful computers, or both.
Something to keep in mind though, is that since mining gives you money, you’ll face competition. After all, who wouldn’t want to receive money? But the more people mining, or put differently, the more computing power competing for the same price, or the more people buying lottery tickets, the harder it is to win.