Sizing or size is any one of numerous specific substances that is applied to or incorporated in other material, especially papers and textiles, to act as a protecting filler

Filler (materials)

Fillers are particles added to material to lower the consumption of more expensive binder material or to better some properties of the mixtured material...

 or glaze

Coating

Coating is a covering that is applied to the surface of an object, usually referred to as the substrate. In many cases coatings are applied to improve surface properties of the substrate, such as appearance, adhesion, wetability, corrosion resistance, wear resistance, and scratch resistance...

.
Sizing is used in papermaking

Papermaking

Papermaking is the process of making paper, a substance which is used universally today for writing and packaging.In papermaking a dilute suspension of fibres in water is drained through a screen, so that a mat of randomly interwoven fibres is laid down. Water is removed from this mat of fibres by...

 and textile manufacturing

Textile manufacturing

Textile manufacturing is a major industry. It is based in the conversion of three types of fibre into yarn, then fabric, then textiles. These are then fabricated into clothes or other artifacts. Cotton remains the most important natural fibre, so is treated in depth...

 to change the absorption and wear characteristics of those materials; it is used as a surface preparation for gilding

Gilding

The term gilding covers a number of decorative techniques for applying fine gold leaf or powder to solid surfaces such as wood, stone, or metal to give a thin coating of gold. A gilded object is described as "gilt"...

; and it is used by painters and artists to prepare paper and textile surfaces for some art techniques.

Sizing also refers to the process of including or applying the substance.
Sizing is used during paper

Paper

Paper is a thin material mainly used for writing upon, printing upon, drawing or for packaging. It is produced by pressing together moist fibers, typically cellulose pulp derived from wood, rags or grasses, and drying them into flexible sheets....

 manufacture in order to reduce the paper's tendency when dry to absorb liquid, with the goal of allowing inks and paints to remain on the surface of the paper and to dry there, rather than be absorbed into the paper.