One of the first things we learned in macroeconomics (it was literally in the first chapter of my textbook, by this guy) was that Gross Domestic Product (GDP) is the market value of all final goods and services made within the borders of a country in a year.
GDP calculation is (relatively) easy when all production occurs within a single country within a single year. International trade and work across years complicate matters, and one common solution is to use a "value-added" calculation.
Consider a simple case: Elbonia has only one product, cogs. In 2007, they produced 100 cogs, which sold for $2 each. Elbonia's 2007 GDP was $200.
Slightly more complex: Kneebonia has only one product, widgets. Each widget is made of 10 cogs. In 2006, they entirely produced 100 widgets, which sold for $50 each, and had widgets in process consisting of 10 cogs at the end of the year. In Kneebonia, cogs are generally valued at $3 each. Kneebonia's 2006 GDP was $5,030 (100x$50 + 10x$30). In 2007, Kneebonia produced 100 widgets, and had no widgets in process at year-end. Kneebonia's 2007 GDP was $4,970 (99x$50 + 1x$20 for the value added in 2007).
International trade: In 2008, the Kneebonian executives realize that, rather than manufacture their own cogs for $3, they can import them from Elbonia for $2 and pocket the difference. Elbonia makes 2,000 cogs at $2 each, for an Elbonian GDP of $2000. Kneebonia makes 100 widgets, but because they didn't make the cogs, they only get to take credit for the value added of $30 per widget, so even though they maintained their widget production, Kneebonia's GDP decreases to $3,000.
So what did the BLS do wrong?
Well, the US has had an awful lot of outsourcing and offshoring lately. In some cases, the cogs were outsourced, and the BLS didn't adjust for the value added. In some cases, it appears that the entire widget assembly was outsourced, and the BLS just kept counting it.
What does it mean?
If the BLS has been consistently overestimating US GDP, it means that actual GDP growth has been less than reported, and recessionary declines greater. By itself, this doesn't necessary make a huge difference, although it may partly account for recent "jobless recoveries", but when factored together with the systematic undercounting of inflation and unemployment, which I've previously mentioned, it adds up to a much worse economic picture than the government has been reporting.