Tyr (pronounced like the English word “tier”; Old Norse Týr, Old English Tiw, Old High German *Ziu, Gothic Tyz, Proto-Germanic *Tiwaz, “god”) is a Norse war god, but also the god who, more than any other, presides over matters of law and justice. His role in the surviving Viking Age myths is relatively slight, and his status in the later part of the Viking Age may have been correspondingly minor. But this wasn’t always the case. Other kinds of evidence show us that Tyr was once one of the most important gods to the Norse and other Germanic peoples.
–from Norse Mythology for Smart People by Daniel McCoy
Little remains documenting the achievements of Tyr. A note in the translation by Henry Adams Bellows of Hymiskvitha, The Lay of Hymir in the Poetic Eddas, indicates that the two great achievements of Tyr, the god of battle, were “thrusting his hand into the mouth of the wolf Fenrir so that the gods might bind him, whereby he lost his hand . . . , and his fight with the hound [of hell] Garm in the last battle, in which they kill each other.” 
Tyr’s sacrificing of his hand parallels Odin’s sacrificing of his eye in some ways. Where Odin’s sacrifice was in search of wisdom, Tyr’s was in defense of justice. For if the gods had succeeded at binding Fenrir through trickery, there would be no justice in their actions.
While references to Tyr are scant in the Poetic Eddas, there is evidence that the Romans knew of him and considered him to be the same god as Mars. The fact that in Latin languages the name for the third day of the week (Mardi in French, martes in Spanish, martedì in Italian) is based on the name of Mars, in Germanic languages the name for the same day (Tuesday in English, Dienstag in German, tirsdag in Norwegian and Danish, tisdag in Swedish), is based on Tyr, though the German version relies on a Latin version of the name for Tyr and the others go back to an alternate spelling, Tiw.
One of the runes in the Futhark alphabet (named by spelling out the first letter of the names of the first six runes where th represents one rune) is Tiwaz, the Proto-Germanic spelling of Tyr’s name. The rune means victory and honor. This connection with Tyr represents both his status as a god of war and of justice.
Many names referred to in the Poetic Edda end in “tyr” which in that context means “god of.” For example, Hangatyr, one of the Odin’s names, literally means the “god of the hanged.”
In other words, he must have been an important god, though few tales remain.
 de Vries, Jan. 2000. Altnordisches Etymologisches Wörterbuch. p. 603.
 Orel, Vladimir. 2003. A Handbook of Germanic Etymology. p. 408.
 Bellows, Henry Adams. 1923. Poetic Eddas p. 102