Short answer: The wolf was one of five standards which represented the four legions of the Polybian era, consular army and was replaced by the eagle in 104 B.C. during the Marian reforms.

Long answer:

After the defeat of Rome’s Latin neighbors, the army expanded to include four legions by 311 B.C. These four legions carried five banners included the boar, the wolf, the minotaur, and the horse. ^1 During this time, the Roman army included several allied Latin contingents and saw the military transform into a manipular army, largely due to the Samnite wars in the late 4th and early 3nd centuries B.C. ^2 Although its tactics changed, the Roman legions would still be organized slightly different, for example, the allied legions often had larger contingents of cavalry than their Roman counterparts.

In the late 2nd century, migrating German tribes, Cimbri and the Teutons, invaded the Rhone valley and defeated a Roman army at Arausio, inflicting its worse loss since the Battle of Cannae one hundred years earlier.^3 Because of this, a new statesmen named Gaius Marius was elected to his second consulship and started to rebuild the Roman military in order to better adept to the challenges Rome faced.^4 He instituted many reforms, marking the beginning of the Roman army’s transition from a largely militia force into a disciplined and motivated professional military. One of these changes included replacing the standard of the legions. Goldsworthy remarks,

“The new legions were much more permanent, keeping the same name and number throughout their existence. In the past each legion had carried five standards, an eagle, horse, bull, wolf, and boar, but Marius gave each legion a single silver eagle as its standard.”^5

It should be noted that the silver standard changed to gold decorated standard by the era of the Principate.^6

In addition, the Social War (91 B.C. to 88 B.C.) created a rift between the Roman legions and its ally legions (called alea). Many of Rome’s Italian allies still did not have Roman citizenship, but by the end of the war, virtually all the communities south of the Po River were granted citizenship. As a result, the alea disappeared; Rome recruited and organized all of its legions in a similar way. ^7

In summary, the eagle became the symbol of the Roman legions, replacing earlier standards which represented Roman and allied legions who had different organization and civic rights. This changed helped mainstream the army and illustrated its change from a coalition of Italian militias into a professional military.

Sources

1. Boak, Arthur, and Sinnigen, William. A History of Rome to A.D. 565. New York: Macmillan Publishing, 1977.

2. Goldsworthy, Adrian. The Complete Roman Army. London: Thames and Hudson, 2003.

3. Goldsworth, Adrian. Roman Warfare. London: Cassel & Company, 2000.

4. McNab, Chris. The Roman Army: the Greatest War Machine of the Ancient World. Oxford: Osprey Publishing, 2010.

Footnotes

1. Chris McNab, The Roman Army: the Greatest War Machine of the Ancient World, (Oxford: Osprey Publishing, 2010), 28-29.

2. Adrian Goldsworthy, Roman Warfare, (London: Cassel & Co, 2000), 39.

3. Arthur Boak, and William Sinnigen, A History of Rome to A.D. 565, (New York: Macmillan Publishing, 1977), 179.

4. Boak and Sinnigen, A History of Rome to A.D. 565, 180.

5. Adrian Goldsworthy, The Complete Roman Army, (London: Thames and Hudson, 2003), 47.

6. Goldsworthy, The Complete Roman Army, 134.

7. Goldsworthy, The Complete Roman Army, 47.

Are you asking about it's use as a military standard, or in general?