The Block Group number is simply the first digit of the four-digit Block number. Thus, all the Blocks that begin with the same digit within a particular Census Tract comprise a Block Group. No Census Tract will have more than nine Block Groups. The Block Group generally is the lowest level of geography you're likely to want for any large-scale analysis for such stories as changes in residential segregation. The boundaries of these relatively permanent statistical subdivisions of a county are designed to change little from one census to the next.
Tracts also are a good size for newspapers that want to map demographics in a metro area.
The reason is that Tracts are small enough for good resolution, but also large enough for shading differences to be seen. You can visualize a Census Tract as something a bit smaller than a typical ZIP Code. Typically, a Tract will have a population of 1,500 to perhaps 8,000, with an optimal size of about 4,000 residents. For the 2000 Census, every part of the country will have a Census Tract number. Within a county, Tract numbers range from 0001 to as high as 9999.