Write the series as x(t) = a x(t-1) + e(t). If a is less than 1, shocks fade and the series pulls back toward its mean. If a equals 1, there is a unit root: each shock is added to the level forever and the variance grows without bound.
Most price series behave as though a is 1 or very near it. That is why buy-the-dip on price levels alone has no statistical basis: there is nothing for it to revert to. Spreads between related instruments, however, can have a below 1 and therefore a genuine mean-reversion-half-life.
Testing for it matters because the difference between a = 1.00 and a = 0.97 is invisible to the eye on a chart and is the entire difference between an untradeable and a tradeable series.
Related: adf-test, stationarity, random-walk, mean-reversion-half-life