The minimum payment is the smallest amount a credit card issuer will accept each month without treating the account as in arrears. Pay at least that and the card stays in good standing; pay only that and the balance can take many years to clear, because most of each payment goes on interest.
How it is set depends on where you live. In the UK, CONC 6.7.5R requires the minimum on a credit or store card to cover the interest, fees and charges applied to the account plus 1% of the balance. On a £3,000 balance charged 2% interest a month, that is £60 of interest plus £30, a minimum of £90, and only the £30 reduces what you owe. Elsewhere the issuer writes the formula into the card agreement, typically a percentage of the balance with a fixed floor. Where the interest is taken out of that percentage rather than added on top, even less of each payment reaches the balance.
Because the minimum is a share of a falling balance, it falls too, and that is what stretches the debt out: as the balance shrinks the payment shrinks with it, and the last few hundred pounds take years. UK rules add a check. Under CONC 6.7.27R, if over 18 months you have paid more in interest, fees and charges than in principal, the card company must tell you so and encourage you to contact it and a free debt advice body.
The credit card payoff calculator applies each country's own minimum payment convention, sets it beside a fixed payment of your choosing, and gives the months to pay off and the total interest for both. Fixing your payment at the first month's minimum and keeping it there, instead of letting it fall with the balance, is the simplest change that shortens the debt.