Definition:
A variable spread is a spread that is not constant in value. A variable spread will condense and widen as market conditions and liquidity change. When the forex markets get volatile, a variable spread will get larger. If the spreads are normally 2 pips on a pair, and suddenly there is a large buying spree on that pair, the spreads would "widen" to something like 5 pips.
The larger spread helps to protect the broker from losing money if there is a delay between the time you clear the order with your broker and the time they clear it on the interbank market.