As a casual player, I'm not familiar with much of the abbreviations and jargon used, so forgive my stupid question: what do LI and rep booster mean?
Poster above answered. Legendary Item (LI) can be obtained at lvl 45 (minimum, the quest is 50) by doing the introduction to Moria instanced area to the end. It can be found by talking to a dwarf in Echad Dunnan (eregion), in front of a "loading" gate.
Every class have 2 of them, and they are class based. Always the main weapon (so, bow/crossbow for hunter, melee weapon for guardian...) and a secondary item (book for minstrel, melee weapon for hunter....).
Those item are different compared to the regular item you are used to, as they get the regular bonus (like agility, moral....) but also are customizable and add bonus to your skills and class playstyle. Every 10 lvl or so, you can reforge them, and they upgrade to become basically the best the level can offer in term of raw stats. Essentially, you'll keep them forever with you.
Due to their nature, consider that once you get them, that's 2 items you will never change (just upgrade over time).
Eventually it's a bit complex and I won't go into details. The questline to get them also act as a tutorial for it, and then you have guides and wiki articles on it.