Returns themselves are close to unpredictable, but their magnitudes are highly persistent. This is one of the most robust empirical facts in finance.
It means volatility is forecastable even when direction is not - which is the entire basis of GARCH-family models and of much of options trading.
Consequences. It produces fat tails in unconditional returns even when conditional returns are normal, since mixing normals of different variances yields a heavier-tailed mixture. It also makes constant-variance assumptions untenable across long samples.