A cedilla is a hook (¸) added under certain consonant letters as a diacritic mark to modify their pronunciation. The tail is the bottom half of a miniature cursive z or yogh: ȝ (). The name "cedilla" is the diminutive of the old Spanish name for zed, ceda. An obsolete spelling of "cedilla" is "cerilla" because the letters d and r were interchangeable in 16th-century Spanish.
The most frequent character with cedilla is the ç (c with cedilla). This letter was used for the sound of the affricate [ts] in old Spanish. Contemporary Spanish does not use it anymore since an orthographic reform in the 18th century.
C-cedilla was adopted for writing other languages, like French, Portuguese, Catalan, unofficial Basque, Occitan, and some Friulian dialects, where it represents /s/ where "c" would normally represent /k/ (for example, while ca is normally pronouced as /ka/, ça is pronouced as /sa/); or Turkish, Albanian, Azerbaijani, Tatar, Turkmen, Kurdish (at least the Mahabad dialect), and some Friulian dialects, where it is used for the sound of the affricate [tS] (the same of English in church). It is also used in a Romanization of Arabic.
And the s-cedilla, ş, represents /S/ (as in show) in Turkish, Azerbaijan, Tatar, Turkmen, and Kurdish. It is also used in some Romanizations of Arabic, Persian, and Pashto, for the letter ar_r.
In the Turkish alphabet both Ç and Ş are common letters, not a variant of C or S.
A few words used in English have a ç, almost all of which are borrowings from French. The most common English word taking a cedilla is probably "façade".
The Romanian Ș (ș) seemingly resembles the Turkish s cedilla, but it is actually a comma. While it is common in online contexts (such as Wikipedia) to use Ş/ş and Ţ/ţ in writing Romanian, that is only because they look almost right and are much more widely supported in character sets. The orthographically correct characters are Ș/ș and Ț/ț (may not appear on your browser).
The diacritics on the Latvian letters g, k, l, n, and formerly r are considered by some to be cedillas and others to be commass.