Romanized in JSL as "soo desu ne", this is a Japanese expression of confirmation. It corresponds roughly to "isn't it" in English and maybe "n'est-ce pas" in French. It indicates a weak agreement with a statement by another person, such as in the following exchanges:

Ii o-tenki desu ne.
-- Soo desu nee.
Nice weather today, eh?
-- (Yes, it is,) isn't it.

Kono kanji wa yomenai desu kedo...
-- "Kuukoo" no "kuu" desu ne.
Soo desu ne.
-- Sore wa muzukashii desu ne.
Soo desu ne.

I can't read this kanji, but...
-- It's "KUU" as in "KUUKOO" (airport), isn't it...
(Yes, it is, )isn't it.
-- That one is difficult, isn't it.
(Yeah, it is,) isn't it.

Ne is a sentence-final particle that acts as a confirmation seeker. Oddly, Japanese soo is roughly the same as English so in meaning, although it is sometimes used differently. Please see these particles for more information.

Note that soo desu ne is different from soo desu ka and soo desu yo, and entirely different from soo desu, depending on the context.