Can you help me understand how I can estimate the variance of a variable?
Variance is the sum of all deviations from the mean. It quantifies the average dispersion of the sample under consideration. It can alternatively be viewed as the average L2 distance between the sampled sites and the mean.

V = ( Σ (x-μ)² ) / N

where V is the variance. x is a sample, μ is the mean and N is the number of samples.
Is variance the same as sum of squares error?
No, as the sum of squared errors is just calculated as Σ (x-μ)². To get the Variance from the sum of squared errors, you need to divide by the number of samples, which is called N here.