This is quite simple, I personally didn't know about this until a friend told me.
Basically, there are items that have the stat of "Reduced Level Requirement". Which basically means it reduces the level of the item by an X amount. The highest that this stat can be is 18, which means that you have to be atleast level 42 to wield level 60 items.
All items, except for Rings & Amulets can have this property (It's great if you find an item that has +resistance or +2500 life on health globe).
Here is a screenshot of what I am talking about.
As you can see, at level 44 you can have a 500 dps weapon, if you have the gold, you can buy 1000+ dps weapons, although they go for quite a bit.
This makes leveling a whole lot easier.