terra sigillata:
1. (Latin.) literally, "stamped earth"
2. A class of Roman1/Mediterranean ceramic fine ware. It is characterized by its firing process the facts that it is fine ware, usually reddish/orange or brown slip, and that it has "stamped" decorations. It dates are disputed, but it began appearing roughly as early as 300BCE, and certain types are proposed to have continued into the 8th Century. Generally speaking, the more Western sigillata had decorations stamped around them, and the Eastern had manufacturer's symbols on the bottom.

Best I can figure this stuff completely replaced "Campanian wares" in the east Mediterranean by 150BCE. It's thought to be based on Etruscan pottery called "bucchero." Both bucchero, and Campanian are much darker than terra sigillata.(Campanian is largely based on Greek "black wares.") Terra sigillata was fired in an oxidizing atmosphere, and by 40BCE Some towns (Arezzo in particular) were firing up what are now some of our notable examples of beautiful glossy fine-ware. We call Arezzo's stuff "Arretine ware."

Speaking of what to call stuff, for earlier periods, terra sigillata is most commonly called "Samian pottery"2, but for some reason, scholars seem to slip into calling it "Red slip-ware" from about 150CE on. The study of terra sigillata has defined as many naming schemes as it has sub-classes of this pottery. If I get a chance to go into specific types you'll see this, the names get crazy. Really.

The good news is that somewhere in the seventies, the naming people finally decided to make peace, and rather than change the name of a type of pot every time they found a new pot piece and changed whence they thought it came, they'd just name them A,B,C,etc... and leave the letters the same if they changed their minds. So our current system goes by provenance and then a letter, which sometimes has a number under it, like so:

African sigillata
Campanian Fine Ware:
   Campanian A
   Campanian B
      Type 1
      Type 2
      Type 3
   Campanian C
Central Gallic sigillata
Eastern sigillata3
   Type A (ESA)
   Type B (ESB)
   Type C (ESC)
   Type D (ESD)
Italian sigillata
South Gallic sigillata

Each area has several types, but I only listed types I'm familiar with to serve as examples.

1"Roman" meaning "from the Imperial Roman time period"... not specifically from geographical Rome.
2note: "Samian" ware (vasa samia), signified a varnishing technique, not that it was a product of Samos.
3"Eastern" in this case means the eastern Mediterranean & Aegean Sea area, the Greek Isles, Asia Minor, Egypt, and Africa. Some scholars exclude Africa and/or Egypt.)

Much of this knowledge was pulled from the head of "my girlfriend the archaeologist" and a much more in depth discussion of it will hopefully appear on SUNY Buffalo's web site.