Can someone please explain why clustered standard errors ensure that the error estimates of Pooled OLS results are appropriate?
Which standard errors are appropriate depends on the properties of the error term. Clustered standard errors are robust to heteroskedasticity and serial correlation in the error term. In that sense, clustered standard errors are "appropriate" when you think this is the case in your context, as they still give you valid inference. One likely reason in panel data for (positive) serial correlation in the error term is the presence of time-invariant unobservables. However, if there are such time-invariant unobservables, other estimators might be more appropriate than pooled OLS, e.g. fixed effects if you think the time-invariant unobservables are correlated with your regressors, or random effects if you think there is no such correlation.