MOB stands for municipal over bond.
The MOB spread is the difference in price between municipal bond futures and Treasury bond futures. The muni futures contract is the "municipal" in MOB, and the Treasury contract is the "bond."
When the muni contract is rising faster (or falling more slowly) than the Treasury contract, the MOB spread will rise, or widen. Conversely, when the Treasury contract is outperforming the muni contract, the MOB spread will fall, or narrow.
To profit from a rising MOB spread, a trader would pair a long position in the muni contract with a short position in the Treasury contract. Even if both contracts went up in price, as long as the muni contract outperformed the Treasury contract the trade would be profitable.
Conversely, to profit from a falling MOB spread, a trader would pair a short position in the muni contract with a long position in the Treasury contract.
The Treasury contract tracks the price of a 30-year Treasury bond (though not necessarily the most recently issued, or on-the-run, 30-year). The muni contract tracks the price of an index of muni bonds.
Interest rates are a major cause of shifts in the MOB spread. That is because the Treasury bond tracked by the Treasury futures contract is noncallable. By contrast, most muni bonds are callable. When interest rates fall, noncallable bonds outperform callable bonds. So when interest rates fall, the MOB spread typically falls.
Changes in the muni index can also cause of shifts in the MOB spread. The index is regularly reconfigured to incorporate newly-issued munis and kick out older bonds. The makeup of the index determines how it will respond to changes in interest rates. So changes in the pace of new issuance and in the average quality of new issues can affect the MOB spread.