Soncino is a publisher that specialises in Jewish books. They are based in Brooklyn, New York.
They are most well known in the UK for their two editions of the Chumash, the "Old Testament" (this is a term religious Jews don't like to use, as it implies the importance of the New Testament). The two editions contain the same Hebrew text and English translation, but different commentaries.
The older edition, editted by former Chief Rabbi Hertz, has a commentary written by him, drawing on various sources, including non-Jewish commentators. Although he was criticised for this, he quoted from the Talmud to justify it - "Accept the truth, from wherever it comes".
When the time came to produce a newer version, rather than repeat what had been done before, the commentary this time was a digest of various other commentaries, including some of the most well known Jewish commentators such as Rashi and the Rashbam.
Apart from the Chumashim, Soncino have produced books containing most of the other books in the Old Testament, again with various forms of commentaries. They also have a range of "non-litturgical" books, on a wide range of Jewish topics.
They are also well known for producing a complete edition of the Talmud with a (somewhat archaic) English translation. This is particularly useful for those who want to start learning Talmud, as being written largely in Aramaic, even an understanding of Hebrew isn't necessarily enough. But it is important to understand the Talmud in its original language to get the real meaning.
Their most recent "new publication" has been the complete text of the Talmud on CD-ROM. This allows people to search through the entire content (which runs to 30 large volumes) in both Hebrew/Aramaic and English.