I tend to mix these up pretty badly. This is in relation to the randomn walk model. The randomn walk model is assumed to have a constant variance but not a finite variance. Without a finite variance, it would imply that the variance of X could grow indefinitely without upper bound as T gets bigger.
But how is this related to the constant variance assumption?
Some reverse logic might be able to help you out. If a variable grows unboundedly it obviously isn’t constant or finite.
Since you already know that we need the variance of the time series to be the same value (i.e. constant) across all observations and this is clearly not the case for a non-finite variable, you know that you breached the stationarity assumption and are into random walk territory.