According to SIFMA, the US bond market is valued at around $40 trillion. With the world-wide bond market valued at just over $110 trillion, this makes the US market account for approximately a third of the entire world-wide market.
The second largest bond market in the world is in Japan with roughly 14% of the world-wide market. Between the US and Japan, they account for a majority of the bond market.
Bond markets determine the price in terms of yield that a borrower must pay in order to receive funding. In one notable instance, when President Bill Clinton attempted to increase the U.S. budget deficit in the 1990s, it led to such a sell-off (decreasing prices; increasing yields) that he was forced to abandon the strategy and instead balance the budget.