What is a Closure?
A Closure is a hairpiece that allows you to have NONE of your natural hair out, yet have a natural looking part in your weave
You will be able to look "natural" while having ALL of your hair braided...
Closures are made out of different bases, some are made out of lace material or some with "thin skin".
I wear lace, and silk base.

The closure is attached by sewing it on to a cornrow base or by attaching it to your forehead with an adhesive (just like a lacefront wig/lacefrontal piece)...
In GENERAL a closure piece is usually used for sew in installs/applications. If placed properly just behind the hairline, it can allow the wearer to wear a full weave with no hair left out while giving the appearance of a natural scalp area.

Closures do not run temple to temple. Instead they are placed in the “horseshoe” area at the top of a weave to close off the style. (Hence the name closure)
Closures are constructed from a number of materials:
Breathable closures are constructed from silk mesh with a poly strip or thin skin around the outer perimeter of the mesh which strengthens the mesh (for a sewn-in application) or to make bonding the closure easier. These closures allow for freestyle parting along the cap area. The addition of a flesh colored fabric under will help to add the look of a natural scalp to this style of closures. This type of closure may require the sealing of the knots (as in a lace frontal) to help keep the hair secured firmly in the base.
Some vendors also construct closures from lace similar to or slightly heavier than a lace frontal. Lace based closures are installed like other closures, but may not look as natural when parted as they will tent to have a “grid” like appearance in contrast to the braided foundation they are installed on top of. Lace closures will required some minor work to achieve a natural appearance. (Bleaching knots, the addition of a of a flesh colored fabric under will help to add the look of a natural scalp to this style of closures) This type of closure may also require the sealing of the knots (as in a lace frontal) to help keep the hair secured firmly in the base.
A few vendors use a combination of stretch lace and flesh colored French silk to create a breathable closure which looks like natural skin. The “skin” can be dyed to match the wearer’s own natural skin.
While not nearly as popular these days, some vendors continue to manufacture and sell non breathable closures. These closures are usually a silk mesh top with a full flesh colored poly coating or full flesh colored vinyl skin top (which was once popular in older style wigs)

Please Check out these sites for more information!
http://forum.blackhairmedia.com/forum_posts.asp?TID=57075
http://divahairtalk.overthehillweb.com/index.php?option=com_content&task=view&id=27
some information was cited from divahairtalk.com
How is it installed?
Closures can be installed by bonding, as well as by attaching with the use of clips. The most popular method for installing closures is by sewing the closure then installing the rest of the weave around the closure.
The closure is placed close to the edge of the braided foundation near the hair line.. The stylist then sews around the perimeter of the closure taking extra care to stitch so that the stitches are concealed.. (a skilled stylist can do this without needing to use invisible [AKA nylon] thread)

Depending on the desired finished style, some of the wearer’s own natural hair may or may not be left out near the perimeter of the front edge of the closure to help conceal the front edge.
Pictures from silkbaseclousers.com(these are just for informational use only!
1. Texture Isn’t An Issue: Closure pieces come in
every texture you could possible think from Silky Straight remy to
Afro-Curly Mongolian. So let your hair down and experiment with
different textures that you usually shy away from due to the difficulty
of trying to create that perfect blend.
2. Versatile Parting:
If you invest in a quality lace base closure be ready to fool the world
into thinking your weave is au naturale. Lace base closures are
designed with medium density and bleached knots to give off the
appearance of a natural scalp. Also, allowing you the option to part
anywhere on the closure, as well as pull your hair off your face while
still creating the effect of a natural hairline.
3. Color Is A Go: Ladies with the closure piece you
no longer have to worry about damaging your real strands trying to
color match your weave to your leave out. Although most lace closures
come in natural black and natural brown, the closure itself still has
the cuticle in tact, giving you the ability to chemically lighten or
darken it to your desired color without causing any damage to your weave
or real hair.
4. Low Maintenance: We can’t think of anything else
more low maintenance than being able to protect your strands while
having absolute styling versatility. Besides the normal cleansing of
your hair and scalp every 1-2 weeks, and everyday styling and
maintaining, adorning a closure requires very little to no maintenance
depending on how you install it. Simply wrap your hair or wear a bonnet
at night and you should be all set!
5. Perfect Protective Style: The sole fact that your
hair is completely braided and protected underneath your weave and
closure allows for optimum protective styling. Allowing your crown the
break it needs from everyday wear and tear such as flat-ironing, product
build-up, excessive styling, sun damage, etc. Like the rest of your
temple, sometimes your hair just needs a break!