NFTs are minted, the term comes from the old way of creating physical coins they were created using a minting press.
Due to NFT being a crypto based technology the term has carried over in that you are minting/creating the token part of the Non-Fungible Token.
In days past crypto was focused on currency such as Bitcoin and Ethereum, a payment system initially designed for low cost fast internet based transactions. The term minting is a direct reference to that, money is also minted. In the United Kingdom they have the Royal Mint which is responsible for the physical printing of money be it coins or paper.
In the NFT world minting is simply a term for creating a NFT. When you purchase an existing NFT you are not minting it, you are transferring it. Minting only happens once at its initial creation.
When you mint a NFT there is a transaction fee associated with the process this varys from blockchain to blockchain some cost pennies some blockchains like ethereum can cost a lot more the fee is referred to Gas.
Gas is constantly moving based on how busy the network is however you can find quieter times when Gas fees are low. These are usually out of office hours like 3am or weekends. Finding times when gas is low can be tricky sometimes you just have to click confirm and mint the NFT before someone else does.