A wand is an indespendable piece of equipment for any witch or wizard. It has the power to magnify magical powers to the fullest degree. A witch or wizard is born with magical powers and the wand has the ability to greaten it.
According to JK Rowling herself:
I been asked what would happen if a Muggle picked up a magic wand in my world. And the answer would probably be something accidental ... possibly quite violent. Because a wand, in my world, is merely a vehicle -- a vessel for what lies inside the person.
The Wand FAQ
If I can perform magic without it, what's the point?
Now, now! See here, according to JK Rowling herself:
You can do unfocused and uncontrolled magic without a wand (for instance when Harry blows up Aunt Marge) but to do really good spells, yes, you need a wand.
Convinced?
I lost my wand! Can I still brew potions?
No. There is always some sort of magical component to potion-making aside from ingredients. Another JKR quote:
there is a magical component to the potion, not just the ingredients. So, at some point you’re going to have to use a wand.
In my notes I have many different cores for wands. Essentially, I decided Ollivander's was going to use my three favourites.. So Ollivander has decided those are the three most powerful substances. Other wand makers would choose things that are particular to their country. Because countries in my world have their own particular indigenous magical species.
There are really only two main components of a wand.
Core: The component that makes the wand actually work. See Cores for a full list of existing cores. There's a bit more information on cores here. Wood: The wood can be one of 13. For a list of woods, see the chart. JK Rowling chose the original wands of Harry, Ron and Hermione according to that chart (it is the Celtic Tree Calendar), but Ron got a new wand which no longer abides by that law.
Wandmakers
Ollivander: Creates wands for everybody in Great Britain. Uses Phoenix Tail Feathers, Unicorn Hair, and Dragon Heartstring.
[French Wandmaker]: Creates wands for everybody in France. As far as we know, only uses Veela Hair.
Gregorovitch: A wandmaker who makes wands for somewhere in Europe. As far as we know, only uses Dragon Heartstring.
Dumbledore, Albus: Wood: Elder Length: Unknown Flexibility: Unknown Core: Unknown Creator: Antoich Peverell? Notes: This wand is the Elder Wand, one of the three Deathly Hallows.
Granger, Hermione: Wood: Vine Length: Unknown Flexibility: Unknown Core: Dragon Heartstring Creator: Ollivander Notes: Her wood was chosen using the Celtic Tree Calender (see the chart below).
Hagrid, Rubeus: Wood: Oak Length: 16" Flexibility: Rather bendy Core: Unknown Creator: Ollivander Notes: Snapped in half when he was expelled. Hagrid still has the pieces hidden inside his pink umbrella and uses the umbrella as a wand.
Potter, Harry: Wood: Holly Length: 11" Flexibility: Supple Core: Phoenix Feather Creator: Ollivander Notes: Harry's wand has the same core from the same animal as Voldemort's. Harry's wand was broken on December 24th, 1997 (maybe even early 25th) by Hermione but repaired on May 2nd, 1998 by the Elder Wand.
Riddle, Tom "Voldemort": Wood: Yew Length: 13 1/2" Flexibility: Unknown Core: Phoenix Feather Creator: Ollivander Notes: This wand shares the same core as Harry's wand.
Weasley, Ron: WAND ONE: Wood: Ash Length: Unknown Flexibility: Unknown Core: Unicorn Hair Creator: Ollivander Notes: This wand was broken in 1992 by the Whomping Willow. WAND TWO: Wood: Willow Length: 14" Flexibility: Unknown Core: Unicorn Hair Creator: Ollivander
Usable Cores (there are probably more)
Unicorn Hair
Phoenix Tail Feather
Dragon Heartstring
Veela Hair (Used only by [French Wandmaker], as far as we know.)
Wand Chart (used for only some wands)
JK Rowling's website states this:
I gave Harry a wand made of holly wood back in 1990, when I first drafted chapter six of ‘Philosopher’s Stone’. It was not an arbitrary decision: holly has certain connotations that were perfect for Harry, particularly when contrasted with the traditional associations of yew, from which Voldemort’s wand is made. European tradition has it that the holly tree (the name comes from ‘holy’) repels evil, while yew, which can achieve astonishing longevity (there are British yew trees over two thousand years old), can symbolise both death and resurrection; the sap is also poisonous.
Some time after I had given Harry his holly-and-phoenix wand I came across a description of how the Celts had assigned trees to different parts of the year and discovered that, entirely by coincidence, I had assigned Harry the ‘correct’ wood for his day of birth. I therefore decided to give Ron and Hermione Celtic wand woods, too. Ron, who was born in the February 18 - March 17 period, was given an ash wand (I think I had originally marked him down for beech), and Hermione, who was born between September 2 and September 29, received a vine wood wand (I can’t remember what I originally stipulated for Hermione; possibly I had not specified a wood for her at that stage).
I have only used the Celtic assignations for Ron and Hermione. Hagrid, for instance, has an oak wand though by this Celtic system he should have a wand made of elder; in Britain, the oak is ‘King of the Forest’ and symbolises strength, protection and fecundity; what other wood could ‘choose’ Hagrid? In any case, I liked having a hidden connection between Harry, Ron and Hermione’s wands that only I knew about (until now, anyway).
For those who are interested in the trees assigned to the different parts of the Celtic year, below is the chart that I used. I apologise to any Celtic tree experts out there for any inaccuracies I may have reproduced (I have found slight variations between sources since I first came across this information.)