Tablature was a common medieval and renaissance form of musical notation that could be written for any fretted string instrument. Often referred in modern times as "lute tablature" because of the preeminence of the lute, tablature was also used for viola da gamba, cittern, bandora, and orpharion.
Mensural notation, both modern and period, tells the reader what note to play. Tablature tells the reader which frets to press and which strings to play. This makes tablature extremely instrument-specific, and tablature is useless for an instrument using another tuning.
Tablature is, however, much easier to learn how to read than mensural notation. This is particularly so when compared to period mensural notation, where which line signified which note would change within the piece!
The standard form of tablature came with two variations, known as French and Italian. Italian tablature, like modern guitar tablature, uses numbers to represent frets. 0 is an open string, 1 is the first fret, etc... French tablature uses letters, where a is an open string, b the first fret, etc... It is important to remember, when playing such tablature, that there is no 'j' in the period alphabet!
Another difference is that French tablature, like modern guitar tablature, has the treble-most string represented by the top line of tablature. Italian, however, uses the bottom line of tablature to represent the treble-most string (modern tablature readers would consider it "upside down").
German lute tablature is completely different. Here each fret on each string is assigned a unique value, either a number or a letter. Learning this notation is tricker than standard tablature, but once the letterings for standard chords become familiar it can be read quite fluently.
Tablature is today disdained by classically-trained musicians, but in the renaissance it held a status equal to other forms of notation and was used by amateurs and professionals alike. Much of the early music publishing business (particularly the publishers Adrein Le Roy in France and William Barley in England), catering to aristocratic amateur players, consisted of printed books of tablature.
Tablature declined with the ascent of keyboard instruments and the invention of a simpler form of mensural notation in the 17th century, but never completely disappeared. Modern guitar tablature is the preferred notation of many guitarists to this day.