The Enuma Elish begins with the creation of the universe, originally an undifferentiated mass of water swirling in chaos. The waters divided into fresh and salt. The freshwater formed the god Apsu and saltwater the goddess Tiamat; from their union were born the younger gods.
So she simply represents the sea, whether she is a specific sea is not mentioned. My own take om this is that Enuma Elish is thought to have been written before or during the time of Hammurabi, at which time the Babylonian empire reached the Persian Gulf, so a possibility is that she represented that sea in particular but I cannot be certain of it. She simply is the sea, that big mass of salty undrinkable water. The main rivers of the Babylonian empire also empty in that same sea so Apsu and Tiamat meet near the sea.
As for her description, Enûma Elish includes a thigh, tail, "lower parts", a belly, lips, ribs, neck, skull, head, eyes, nostrils, mouth, and udder. She has blood, insides, arteries, and a heart. Below I have included a snippet from my source where multiple parts of her are described.
And the evil wind that was behind (him) he let
loose in her face.
- As Tiamat opened her mouth to its full extent,
- He drove in the evil wind, while as yet she had
not shut her lips.
- The terrible winds filled her belly,
loo. And her courage was taken from her, and her
mouth she opened wide.
IOI. He seized the spear and burst her belly,
- He severed her inward parts, he pierced (her)
- He overcame her and cut off her life ;
Luzacs Semitic Text and Translation Series (PDF) (Vol XII ed.). p. 150-line 122. (goes directly to pdf which can be downloaded at your leisure)
Now this is probably not the description you're looking for so I will look further into her "Dragon appearance" for which I will use some snippets from Wikipedia (I am getting stressed for time so might finish it on another date).
The pdf I linked above talks more about the nuances of her portrayal as a dragon.
Some scholars clearly see her as a dragon while some disagree as also noted on wikipedia and their sources.
Tiamat is usually described as a sea serpent or dragon, although Assyriologist Alexander Heidel disagreed with this identification and argued that "dragon form can not be imputed to Tiamat with certainty." Other scholars have disregarded Heidel's argument: Joseph Fontenrose in particular found it "not convincing" and concluded that "there is reason to believe that Tiamat was sometimes, not necessarily always, conceived as a dragoness."Fontenrose, Joseph (1980). Python: a study of Delphic myth and its origins.
The Enûma Elish states that Tiamat gave birth to dragons and serpents among a more general list of monsters including scorpion men and merpeople, but does not identify her form as that of a dragon; however, other sources containing the same myth do refer to her as such. King, Leonard William (1902). The Seven Tablets of Creation (Vol. II: Supplementary Texts). p. 117.