[jyl]

Simplify it to a hypothetical 1 year bond.

Bond has printed on it "1 year term, $100 face, and 5% coupon". That means in 1 year ("term") you get one payment ("coupon") of $5 (= 5% interest on $100) and you also get the $100 ("face") when the 1 year is up (the bond reaches "maturity").

If you pay exactly $100 for this bond and hold it until maturity, you will get a return ("yield to maturity" or just "yield") of 5.0%. Pay $100, receive $105, 105/100-1 = 0.050

If you pay $97 for this bond, you will get a yield of 8.3%. Pay $97, receive $105, 105/97-1 = 0.083

If you pay $103, you get yield of 1.9%. 105/103-1 = 0.019

So price moves inverse to yield:

$103 1.9%
$100 5.0%
$97 8.3%

For a real life bond, where there are many years of coupon payments which may be semi-annual or some other period, calculating the yield is more complicated, but the principle is the same. For a given bond, the higher the price you pay, the lower the yield you get.