When you hear that the "stock market rallied," it means that stock prices have moved up. This is a good thing for those people who own stocks since they can benefit from the capital appreciation of these stocks.

But it is a bit more difficult to interpret the rally of the bond market. If you recall, a bond is basically a loan that pays interest. Corporate bonds usually pay interest twice a year to lenders.

If you own a 5-year corporate bond that pays you based on a loan of $1,000 at 10% interest, this means that you will get a total of $100 each year for 5 years. At the end of the fifth year, you will also get your original $1,000 back. Supposing that yesterday you bought this 5-year corporate bond for $1,000 (at an interest rate of 10%) but your friend buys a similar bond the next day but he gets a rate of only 9% because interest rates went down due to action by the Federal Reserve Bank between yesterday and today. Your bond is worth more because you are getting an interest rate of 10%, which is higher than the current rate of 9% any other bondholder will get if she purchased the same type of bond today.

The basic concept here is that once you own a bond that has a set interest rate, your bond looks better and better (i.e. it is worth more and more if you want to sell it) if interest rates go down. (Remember that your interest rate is already fixed so it won't go down as long as you own it). As rates goes down, your bond rallies or is worth more and more. To make a long story short, lower interest rates make bonds you own worth more. In other words, bonds rally with lower rates.