Tabard
A tabard is a simple covering worn over armour (in period, usually maille armour) originally to protect it from heating up in the harsh Middle Eastern sunlight of the First Crusade. It quickly became decorated with embroidery and heraldic display.
Tabards are reletively simple: a cloth rectangle with a hole for the neck. At the waist is was held closed by ties or the swordbelt. Heraldic tabards were often worn without armour, as pure heraldic display.
The surcoat was a more elaborate adaptation of the tabard, and dates from later in period.
Tabards in the SCA
In the SCA tabards are commonly worn over armour in the field or over garb of it. In both cases, they are used as heraldic displays. In the Kingdom of Ealdormere, for example, heralds and guards who attend on the crown wear tabards bearing the kingdom arms.
Because of the ease of construction, many fighters own several tabards. Those bearing the arms of their barony or kingdom are worn when at war, and those bearing personal or household heraldic displays are worn at tourneys.
In A.S. XL, King Aaron of Ealdormere issued a request at his coronation to the Fighting Households of Ealdormere, encouraging them to make and wear tabards bearing the Kingdom's arms in time for the Pennsic War.