An Annuity is a loan with a monthly repayment, which is always the same amount. In other words you pay each month the same sum.
This annuity payment consists of both interest and principal repayment. The composition of interest and repayment changes slightly with each month. This is because each repayment reduces the remaining loan balance. Therefore, with a constant interest rate, and a declining remaining loan balance, the share of interest in the installments decreases month by month, while the share of repayment increases a little month by month.
This goes on until at the end of the loan, the principal repayments are almost 100% of the monthly annuity. In other words your savings component (the repayment of the loan balance) increases, month by month, year by year. The alternative is a linear mortgage. In a linear mortgage your principal repayment remains the same. Therefore your monthly payments goes down months after months. This mortgage form is rarely used, because for most people incomes increase over time. So, if anything, people want their repayments (which are in essence savings) to increase with their income rather then to decline. This is what happens in an annuity.