In the context of clothing, a placket was originally the term for the slit in the collar, waistband, or sleeves of a garment which can open to allow easy dressing. They are usually closed with zippers or buttons.
In modern usage, a placket is most often the double-layer strip of cloth that runs down the center of a shirtfront for buttons fasten through (or, in some cases, to cover a zipper).
A placket may also refer simply to the row of buttons down the front of a shirt; when no placket is apparent on a button down shirt, this is called a 'French placket'; this gives a very minimalist look. If the buttons are covered by a unperforated strip of fabric this is known as a 'covered placket' or a 'fly front', and is often used in more formal shirts, as might be used when wearing a tuxedo.
Shortened plackets are also frequently used, as with three- and four-button plackets on golf shirts and Henley shirts. Decorative plackets often make appearances, particularly in women's blouses and dashikis.
If you are feeling fancy French, you may also spell placket as 'placquet'.