DI+ measures how much of the recent true-range came from higher highs and DI- from lower lows. When DI+ is above DI-, upward movement has dominated. adx is then built from the normalised gap between them.
Crossovers of DI+ and DI- are sometimes traded as entries, usually with a requirement that ADX be above a threshold so that the signal only fires in trending conditions.
Like every Wilder indicator it is smoothed and therefore late, and the crossover version generates many signals in choppy markets. Its more defensible use is diagnostic: seeing which side of the range is doing the work, rather than as a trigger.
Related: adx, true-range, trend-following, whipsaw, momentum-indicator