In the context of Gundam Wing, Heero Yuy refers to not one, but two people. The first Heero was a pacifist leader of the colonies who managed to unite many of them in an alliance, and even inspired Earth nations, like the Sanc Kingdom. Fearing the power that the movement was gaining, the Romefeller Foundation had Heero assasainated. The assasain, Odin Lowe, would then later take into his care a young boy whom he trained. After Lowe's death, the young boy would eventually find his way to the mysterious Professor J, who would train him to pilot the Wing Gundam in Operation Meteor. As he departed for Earth, the Professor chose a code name - the name of the colonial leader killed so many years ago - Heero Yuy.
Fate's funny that way, isn't it?
Heero is supposed to be the analogue to Amuro Ray, but unlike the other characters, who emulate the characters they correspond to, Heero serves as a counterpoint to Amuro. Where Amuro starts as a civilian and becomes a capable officer and commander, Heero begins steeped in the world of war, and seeks to be able to never hurt anyone again. Though Heero seems somewhat suicidal initially, he really isn't - and many scenes later show that he does want to live. Most notable, however, is the fact that Heero can use the Zero System successfuly - most people are broken by it.
Heero initially uses the Wing Gundam, but after it is damaged in a fight with Virgo mobile dolls,he is given the helm of Gundam Epyon. In a battle with Zechs Merquise in the Gundam Wing Zero, the two fight to a standstill, then trade mobile suits. In the final episodes of the series, Heero duels again with Zechs, and manages to destroy the battleship Libra.