OLS remains unbiased under heteroskedasticity, so the coefficient is still a fair estimate, but the reported standard errors are wrong, usually too small. That turns marginal results into apparently significant ones.
The cheap fix is robust (White or Newey-West) standard errors, which correct the uncertainty without changing the estimate. The better fix, when the variance pattern is itself the interesting part, is to model it directly with ewma or garch.
Worked example: a regression reports a t-statistic of 2.4, comfortably significant. Recomputed with Newey-West errors allowing for autocorrelation and changing variance, the same coefficient gives a t of 1.3. Nothing about the strategy changed except your honesty.
Related: ols-regression, residuals, garch, volatility-clustering