Trying to Start in Equilibrium. Good Alternatives to Burn-In. The One Long Run web page explains why we can limit the discussion to just one run. This is the burn-in period. After the burn-in you run normally, using each iterate in your MCMC calculations.
Many electronics components fail quickly.
Those that don't are a more reliable subset. So a burn-in is done at the factory to eliminate the worst ones. Markov chains don't work the same way. Running longer may cure the first, but a dead transistor is dead forever. Asymptotics Contra Burn-In.