Hearthstone players are going to end up with a mountain of cards that are either worthless, uninteresting, or duplicates. Instead of putting them in a virtual bicycle's spokes so that it sounds like a motorcycle when you pedal, you'll have the option to craft cards into new (and hopefully better) ones.
Blizzard sees the crafting system as a better alternative to trading between players, since trading can lead to a pile of cards that nobody wants as everyone chases the most popular ones. With the crafting system, players can simply disenchant unwanted cards for arcane dust and then use the dust to purchase the cards they desire.
You won't be getting a 1:1 trade for cards via crafting. For example, common cards disenchant for five arcane dust but cost 40 to purchase, while legendaries disenchant for 400 arcane dust and cost 1600 to buy. Gold versions of all cards give more and require more arcane dust with the crafting system.