Depilation, by definition means removing hair from above the surface of the skin.
So according to the definition there are two methods that could safely be classified as depilation:
Mechanically: Hair shaving
Chemically: Depilatories or depilatory creams
Methods that remove hair from under the surface of the skin fall under Epilation.
Now what is meant by above the surface is that it has nothing to do with the hair at its root or say at the level of the hair follicle.
Hence depilatory methods are age old practices of hair removal since ancient times. And thus are most suitable for at home hair removal.
On the contrary what is meant by under the surface is that it has everything to do with the hair at its root i.e. at the level of the hair follicle.
Hence epilatory methods could be classified under relatively modern techniques of hair removal. Most of them are performed by trained and qualified professionals and in general are not suitable to be attempted at home.

Well, I don't really think that anybody here needs information about shaving or how to shave. But as it comes under the topic of our discussion, it's opportune to write a line or two about it here.
First and foremost thing to note about this method is that still, while I am writing these lines, it remains the most popular and easiest and cheapest method to remove body hair.
Reasons to this fact are also quite obvious.
Nevertheless, one should not forget that shaving is and never was a lasting solution for hair removal!
In terms of duration, it is the shortest acting option to remove unwanted body hair and is the most temporary method among all. Lasting for a day or two, at max!
Please go here to read more comprehensive shaving tips and techniques for women.

Well, depilatories do the same job as shaving in a chemical way. So I prefer to rather call it the 'Chemical Shaving'.
The depilatory cream or lotion or powder chemically dissolves or breaks down the hair protein to a fluffy mass.
In terms of duration of action, they act a bit longer than that of shaving, say 2-3 days.
The container usually provides you with the instructions on how to use. Usually the cream or lotion is applied over the desired area of the skin and left for the recommended time period and then wiped off.
And if you are lucky, then the unwanted hair will be wiped off either along with the cream or lotion.
I said 'if you are lucky', because depilatories do not work for everybody. Coarse or thick hair may fail to respond to depilation.
Depilation - The Advantages:

Depilation - The Disadvantages:

Things to Remember while Using Depilatories

If you want further detailed product by product reviews of depilatories from the customers themselves, then there is no better place than Amazon to do so.
Need to explore other options to remove unwanted body hair? Well… here's a list of alternatives to depilation for body hair removal.
Wish you all the best in your venture depilation!