Any period of ten years is a decade, including any arbitrary span of ten years; for example, the statement that "during his last decade, Mozart explored chromatic harmony to a degree rare at the time" merely refers to the last ten years of Mozart's life without regard to which calendar years are encompassed.
The most common way to refer to decades is to group years based on their shared tens digit, such as the nineteen-sixties (1960s) referring to the period from 1960 to 1969. This is the definition generally used on Wikipedia. Sometimes, only the tens part is mentioned (60s or sixties), although this may leave it uncertain which century is meant.
An ordinal decade in the Anno Domini[a] year numbering system is a period from a year which ends on the digit 1 to the following year which is a multiple of ten; for example, the period from 1961 to 1970 was the 7th decade of the 20th century (or the 197th decade), and the period from 2001 to 2010 was the 1st decade of the 21st century (or the 201st decade).
Particularly in the 20th century, a nominal decade is often used to refer not just to a set of ten years but rather to a period of about ten years - for example, the phrase the sixties often refers to events that took place between around 1964 and 1972, and to memories of the counterculture, flower power, protests of 1968 and other things happening at the time. Often, such a nominal decade will come to be known by a title, such as the "Swinging Sixties" (1960s), the "Warring Forties" (1940s) and the "Roaring Twenties" (1920s). This practice is occasionally also applied to decades of earlier centuries, for example, references to the 1890s as the "Gay Nineties" or "Naughty Nineties".
^Passim, i.a. Spencer, Donald D. 1989. Invitation to number theory with Pascal. Ormond Beach: Camelot. 46: "The first decade is from one to ten inclusive, the second decade from eleven to twenty inclusive, and so on."