Say you are trying to immunize a 7 year duration liability and have two options, a zero coupon bond with 7 years to Maturity or a combination of a 2 year zcb and a 9 year zcb They both have duration 7,but the 7 year has zero dispersion of its cash flows around its duration because there is just one payment. The two combined zcbs have one payment before the duration and one after, so there are some cash flows that don’t lie on the duration. Think of it like a fulcrum and the two payments are balancing out at 7 years.
Now, if spot rates change at the 7 year, the single payment is affected the same way as the liability so the portfolio remains immunised,it moves in the same way. But the 2 year and 9 year spot rates might move differently and we will have to adjust the portfolio to re immunise.
The dispersion is higher than zero so we have more spot rate moves to monitor to keep our portfolio immunised.
Higher dispersion means more cash flows spaced away from the duration, so a higher effect from yield changes.
Plot the cash flows on a chart and see how spaced out they are. Then imagine having to discount each cash flow with spot rates.