The Operational level of warfare is complicated and often bleeds into the the other levels of war. In essence, its more than just encircling an enemy. The term operations is usually used to the describe the movement of troops in a theatre of war towards an objective laid out by the strategic plan by military's leadership/ state government. It does not include the diplomatic or political notions involved in the strategic level.

The concept we think of as the "Operational" level of war is a fairly new concept. It has roots in the late 1700 and early 1800's with military theorist, and Napoleons campaigns are often regarded as the first "operational" campaigns. Although this subject is quite controversial and arguments can be made that it started earlier with individuals such as Frederick the Great of Prussia or even Gustavus Adolphus of Sweden. However, I would say what we think of today in the modern sense of the word, it has its roots in the 19th century. At this point, it was viewed as Grand Tactics and was seen as the movement of troops and logistics necessary to coordinate an offensive. The credit for the creation of the term "Operations" is usually given to the Soviet Union in the 1920s and 30's with the creation of their doctrine of "Deep Operations" which was used in the Second World war.

An easy way to think about it is tactics is about winning battles and strategy is about winning the war, operations is the thing that links them together. Its moving supplies and men in a theatre of war to the battlefield in a way that advances also towards the strategic goal. Operations aim to turn the tactical success on the battlefield into success on the strategic level. A victory on the battlefield does little to win the war on its own, but if you continue and string together more victories, then it can succeed at the strategic level.

A lot of historians have taken a retrospective look when it comes to the use of Operations and try to retroactively apply it to other wars such as the Romans. However, at the time they would not have seen it that way. While the term "operations" didnt exist, many historians make the argument that it still existed as troops and materiel was moved in the theatre of war to facilitate battle. I would make the argument that what Fabius Maximus was more tactical than operational, as his "Fabian" strategy of not engaging in pitched battle generally does not follow an operation but rather a strategic goal.