The name bet is derived from the west semitic word for "house", and the shape of the letter derives from a proto-sinaitic glyph that have been based on an egyptian hieroglyph.
As a prefix, the letter bet may function as a preposition meaning "in", "at", or "with".
As bet is the number 2 in gematria, this is said to symbolize that there are two parts to Torah: the Written Torah and the Oral Torah.
Rashi points out that the letter is closed on three sides and open on one; this is to teach you that you may question about what happened after creation, but not what happened before it, or what is above the heavens or below the earth.
In set theory, the bet numbers stand for powers of infinite sets.
The written Torah begins with the letter bet ("Bereshit...", at the beginning), the oral one with the letter mem ("Meematai..."). The two letters together form the word bam, of those things. The Shema prayer reads ... vedibarta bam belechtecha baderech.., and you shall speak of those things (and not of others) when you walk on the street. (source: Maghid taaluma).
Below you can see the movie of the big clay prototype production process of a hebrew letter.