In Factions, you take the role of a Summoner. You’re encouraged, though by no means required, to come up with a backstory for your Summoner. Some people on the forums run roleplay campaigns, and staff will periodically try to slip Summoners into lore updates.
You can create your Summoner at this link.
You can also add an entry on the Factions Wiki.
What’s a Summoner?
Having known the scourge of the Rune Wars in our own lifetimes,
and being resolved that future generations should be more fortunate,
we commit ourselves to this great task, upon which our shared future depends:
…to turn the magic that nearly destroyed our world to her protection,
…to seek peace and knowledge by which all nations may together prosper,
…to ensure that the calamity that has been foreseen shall not come to pass.
We hereby bind ourselves with this oath,
…under geas and bond-word,
…taken after solemn contemplation of its grave meaning:
to assist the League’s Champions upon the Fields of Justice,
…invoking only those magics authorized by the Council,
…giving our considered guidance as Champions may request it;
to serve our several nations through the League of Legends,
…in peace and in war,
…in victory and in defeat;
to obey the lawful judgments of the Council,
…above even the laws of our particular sovereigns,
…faithful even unto death;
and so stand now,
Summoners of the League of Legends.
—The Summoner’s Oath
A Summoner is a mage trained in rune magic at the Institute of War. Mere decades ago, nations like Demacia and Noxus used rune spells in horrifically destructive Rune Wars that nearly destroyed Runeterra. After the Fifth Rune War, realizing that very soon there would be nothing left to fight over, they came together to form the League of Legends, an organization committed to preventing another Rune War by containing conflicts and providing peaceful resolution through a sort of trial by combat. (You may be familiar with the particulars; it often involves five Champions on each side of a map.) Linking minds with a Champion and channeling magical energy into them, whether from yourself or from mystical items, is a “safe” form of a type of rune magic that once turned heroes into gods. Similarly, the spells that are cast on the Fields are purified forms of the basic types of rune spells.
This makes Summoners the keepers of rune magic. Ideally, they study it in order to learn how to reverse the damage done to Runeterra. Realistically, everyone understands that the Institute is also an armory of living weapons. If the League should fail, and some believe that is all but inevitable, it is the Summoners who will cast the first rune spells of the next (and very possibly last) Rune War. In other words, member-states want their people trained as Summoners in part because they want to have some “WMDs” on hand if this whole League thing breaks apart.
Becoming a Summoner
This is also the title of a cute Tumblr.
Very few have the talent or training necessary to survive the trials of the Institute of War. The vast majority of Summoners are top mages within their member-states, generally with at least the equivalent of “magic college”, and for that matter “magic grad school”, under their belts. (Summoner candidates already know that it’s “wingardium leviOsah” not “levioSAH”.) They also tend to be from the upper echelons of society, as it takes no small amount of political favor to get one’s name put forward to don the purple and gold.
The process begins with a Judgment, similar to that which aspiring Champions face. Summoners can be a schemey lot, and pure motives are not strictly required. But nor do they want unstable lunatics learning rune magic. Those who pass the test are granted initiate status at the Institute of War.
Summoner training is neither easy nor safe. Every year, some number of initiates die or go mad. There are 30 formal “levels” of training, through which aspiring Summoners learn the deep foundations of rune magic. The classical “Summoner spells” represent, in stylized form, the basic forms of rune spells. Most candidates find that they resonate with one spell in particular, and some develop the ability to use a form of that spell even off the Fields, without resort to destructive runes.
Summoners do vary in their particular talents. Some are primarily diplomats, brokering agreements between member-states or dispatched to perform high-stakes negotiations. Others are scholars, devoting themselves primarily to the study of magic or techmaturgy. And some particularly bold Summoners specialize in combat, whether hunting down monsters (or the occasional rogue Summoner) or leading their member-state’s troops in the wars that the League, for all its efforts, routinely fails to entirely prevent.

(21 CLE) High Councilor Kolminye oversees construction of the Crystal Scar.
A Summoner’s Duties
Summoners may be sent on missions by either their member-state or the Council itself. They might also be approached by a Champion, stereotypically because said Champion needs some research or investigation done. These missions range from chasing down monsters to exploring archaeological sites to mending damage from the Rune Wars to assisting when disasters strike.
And then, of course, there are matches on the Fields. Summoners, like Champions, are obligated to come forward and fight for whichever member-state calls upon them. The details need not be recounted here, but there is generally an exchange of money and favors behind the scenes, and member-states do have to abide by certain arcane rules regarding whom may be called upon when. But the general rule is that it is a free-for-all: as a Champion or as a Summoner, your primary loyalty must be (at least as a formal matter) to the League and its mission, not to your member-state. In some cases, the parties to the dispute are not disclosed until after the match, e.g. where there is especially great concern of bias. (Summoner Lyte of the Riotous Fists Clan was, before his departure in early 26 CLE, particularly infamous for coming down hard upon those few, foolish Summoners who “threw” matches.) When not fighting in actual disputes, Summoners frequently hone their skills in simulated matches conducted using thaumic “imprints” of Champions.

(25 CLE) Summoner and Machine Acolyte 333lom stands by Viktor and Merricurry during the Battle of Shurima.
During Major Disputes
Generally speaking, Summoners must fight for whichever faction calls upon them. However, during major disputes, i.e. the subjects of Factions arcs, Summoners and Champions temporarily proclaim allegiance to a particular side. They serve that side both on the Fields and off. Major disputes often involve actual combat within the dispute zone, and the presence of Summoners can have a significant impact on the course of a battle.