A swash is a typographical flourish on a glyph, like an exaggerated serif.
Capital swash characters, which extended to the left, were historically often used to begin sentences. There were also minuscule swash characters, which came either extending to the left, to begin words, or to the right to end them. They were used in former times to help fit the text to the line, instead of spaces of varying widths (“justification”).
Some of the characters in ligatures were called swash characters, even though they did not protrude to the space on either side of the piece of type, such as the tail of a capital “Q” passing under its succeeding “u”. Similarly the tail of a swash “g” would extend to the left beneath a number of preceding letters limited by the set of ligatures the typographer chose for the set.
An extended flourish on a printed character.