To be boosted or to recieve a boost is to have a player much higher level than the instance is designed for, run a lower level character through it.
For example, the missus boosted me through ZF on her level 70 rogue, when I was playing on my level 45 paladin. The mobs do very little damage to a level 70, meaning my level 45 could sit back and let the level 70 do all the work. Dont beg or spam for boosts, its one of the most annoying things people do. Ask a guildie - you are in a guild and didnt create one just for the bank space, right? :mrgreen:
Boosting is a reasonable way to level up, but is mainly used to get pieces of gear for the lower level character (or to complete quests in your case). Doing the instance with a group of a proper level will net you greater rewards, not only in XP (as being boosted results in much less XP gained by the lower level character), but also it will teach you what to do in a group - Croud control, tanking, healing, etc etc.
Mining/Blacksmithing is useful for a warrior, especially as a first character. More recently, the introduction of Season 1 Arena gear aquirable (sp?) with normal honor points has reduced the usefulness, but still a nice way to get some gear if you dont like PvP. Dont worry too much about this until you hit level 70 though.
*edit - Reading through my replies I see Ive made a few comments that might seem odd. Remember one thing, once you hit level 70 WoW becomes a different game, sure you can quest and kill normal mobs, but a new world of instances, raiding, and PvP open up. Most of my comments are there to make life easy for someone who doesnt have a level 70 character already - having a 70 that can support a new character makes leveling very different to starting from scratch. Some people like the leveling process, and once they hit 70 start a new character. Others (like myself) hate the process and only when I start doing top end instances and raids do I begin to have fun.
*edit2 -
my alt is maxed out at 225 on enchanting & alchemy. nobody wants my lower level stuff & Im still miles away from lvl 35 to up it to 300.
To be honest at that level the stuff you can make
is crap - not your fault, its just the way the game works. Once you get to 375 in those professions (300+ is only available once you install the Burning Crusade expansion pack), you will be able to learn some brilliant recipies. Healing pots that restore 3000 health, enchants that temporarily give the wielder of a weapon 120 agility, etc etc.