A nonstandard dialect is a dialect that does not have the institutional support or sanction that a standardized dialect has.
Like any dialect, a nonstandard dialect has its own vocabulary and an internally consistent grammar and syntax; and it may be spoken using a variety of accents. Describing a dialect as "nonstandard" is not to imply that the dialect is incorrect or inferior. Also prestige dialects may be non-standard.
As a border-case, a nonstandard dialect may even have its own written form, although it's then to be assumed that the orthography is unstable and/or unsanctioned, and that it is not orderly supported by governmental or educational institutions. When used in quotes and as a contrastive feature in literature, the term eye dialect may be used for nonstandard phonemic spelling.
It is uncommon in written texts unless the text is dialect poetry, etc.