Most countries have
progressive taxation regimes, where the amount of marginal tax collected rises at different threshold intervals. Bracket creep is caused when these thresholds do not rise as fast as the nominal value of
incomes,
assets or whatever is being taxed.
As many people enter the highest income tax brackets thinking their salaries reflect the real value of their talents and hard work (and not just because of inflation), they tend to forget that these thresholds are static. So while their incomes after tax may be higher, the prices for goods and services have actually risen faster.
Governments love bracket creep, as it gives them more revenue without having to declare any new taxes. Right wing governments particuarly like bracket creep because it creates a new class of annoyed high tax-paying voters who will probably then align with fiscally conservative politicians.
There are efficiency and equity arguments against bracket creep. The motivation to earn extra income by increasing productivity or working harder is lost when taxes are high. It can also discourage people to switch from welfare-dependency to employment when their lowly incomes suddenly become taxable.
If there is sufficient political will, bracket creep can be solved by instituting a flat tax, or by indexing tax thresholds with inflation.