It’s all in subj line, however, I thought variance of error term correlating with independent variables is serial correlation? Icould somebody throw some light on this?

Serial correlation is when the variance of the error terms are correlated from one period to the next (if you look at the graph you will see that the error terms move in a pattern). Heteroskedasticity is just what you have said, when the variance of the error terms is correlated to the number of independent variables. If you look at this in graph form you would see that the error terms are more closely grouped when their are few independent variables, and then become more dispersed the more variables you add. It really helps to look at a picture…

Serial Correlation: http://www.analystforum.com/article/cfa/serial-correlation

Heteroskedasticity: http://www.unc.edu/courses/2008spring/soci/709/001/soc709%20lec11.htm

Hope that helps.

Technically, heteroskedasticity is when Variance(error) is not constant

This is not about multiple regression, but it is when the variance of the error terms changes in relation to the independent variable. When x is large, the error is large, for example.