Twinking in WoW is where you would use items or item/weapon enchants that would not be available to a low level character with only a little gold.
These enhancements enable a level 10 character to take on mobs three or four levels higher with impunity and hence speed up leveling. Obviously if this is your first, and poor, character you won't have the option, unless you can buy or beg gold.
Assuming you have some spare gold from a previous character or a wealthy friend or guildmate, should you bother with twinking?
Although it will indeed level you faster, I generally don't bother myself for these reasons:
1. It take a good while to gather items or stand around in a city looking for enchants. You can be up a level or two while you hang around waiting for an enchanter to appear.
2. It costs lots of gold that I can use for decent gear later on. The low level gear gets discarded soon enough.
3. It takes away from the sense of achievement in doing it on your own. You may as well employ a paid levelling service.
A couple of things that you should consider, even if you aren't twinking, are the first aid skill and engineering.
Warcraft First aid is fast enough to level – all you need are stacks of cloth. You can get to skill 150 at level 5 without wasting much time. Just buy stacks of linen, wool and silk in the AH. You can then use heavy silk bandages for a fast heal between fights.
Engineering enables you to equip some nice items that are otherwise unavailable. This will still be a useful skill at 60. For example you can't get a head item at low levels but if you have engineering as a profession you can use Green Tinted Goggles right from level five and upgrade them to Master Engineer's Goggles later. You also get to make dynamite and bombs which are useful in dealing with mobs.