What is the difference between diversified and undiversified VaR. Can anyone explain in detail?

Undiversified VaR: Take the sum of the VaR(x) of each individual risk factor.
Diversified VaR: Take the VaR(x) of the joint cumulative distribution function of multiple risk factors.

Diversified VaR describes the correlation benefit which accrues from holding a diversified set of assets. If you set your entire correlation matrix to one's you will obtain your undiversified VaR.

You have a trading book (TB), your diversified VaR is a single PnL vector covering the whole TB,  your undiversified VaR is a single PnL vector for each "material" risk factor traded by all desks. For the whole  VaR (TB) <= VaR (IR) + VaR(FX) + VaR(COM) + VaR (CSR ) + VaR (EQ). The IR, FX, COM, CSR, EQ are interest rates, FX, commodity's, credit spread risk and equity. If the PnL vectors are consistent with the assumption underlying VaR then the above inequality holds-this is called the coherence of VaR, otherwise, if your PnL vectors are not "Normal" or they are heavy-tailed or skewed then the above inequality fails and you need to take that into account.

The usual Assumption is daily returns are independent. The normal assumption comes then from the central limit theorem. Also i think you need some dependence assumption for proving the resulting VaR Measure is in fact coherent.
Of course there are simple Examples, where the Var will not be coherent. One example i found a while ago where 2 risky bonds having the same credit spread/default intensity. And the defaults being iid distributed.

It depends on the percentage of risk at which you can gain a lot.