Ok, couple of quick things to add.
(Just for clairity)
Bonds in general: Bonds are a debt security. Even though bonds come in many shapes and sizes, and are issued by many different types of entities (Corporates, municipalities, states/provinces, public utility companies, sovereign governments, etc...,) for the purposes of this inter-market analysis in cash/forex, we are focused on US government bonds at various maturities.
Maturities are when the bond is set to 'mature/expire' and is repaid in full by the issuing party. The longer time horizon to maturity, the more risk is involved since there's more time 'into the future' of unknown events for something to go wrong that might affect the bond's value. So generally speaking, unless the market strongly believes there will be lower interests rates in the future (which is called an inverted yield curve, which I will talk about later,) the further you go out in maturity times the more the bond will yield.
Bond Yields, and effective yields, come in two components: The coupon rate set on the bond at issue, and the bond's par value in the active market.
There is an inverse relationship between bond prices and interest rates. This is because a bond's price in the active resale market reflects its fair value when compared to all other bonds currently available. Should newly issued bonds have different a different yield (coupon rate,) for the same time to maturity, then existing bonds in the market must be repriced to reflect the current market rate.
For example: If interest rates rise, existing bonds must be priced lower than their face value (being what is paid out at maturity) to make up for the difference in interest paid on the coupon. The buyer then gets the capital gain between what they paid for the bond and what the bond issuer pays out to them at maturity in order to make up for the lower interest rate they were paid during the life of the bond. Inversely, if interest rates fall, then older bonds are clearly more attractive since they still pay out the higher rates from the past, and thus the price of the bond could rise above their face value to compensate (meaning someone is going to pay more than par on the bond, but the capital loss they realize when the bond matures is covered by the higher coupon they received while holding the bond to maturity.)
Interest rate futures (or financial futures) as we've been looking at in this thread are tracking the interest rates and values of various federal bonds and their respective times to maturity. They are NOT actual bonds in themselves, but a futures contract on the value of such bonds. That means we can track them for the information they give us on bond yields and prices, but we can't trade them directly expecting them to behave and act like a bond.
For instance: If you go long the front month 5 year interest rate futures contract, it would expire within 3 months unless you rolled it forward into the next futures contract, not in 5 years like a bond would if you were to buy the underlying US 5 Year note. As well, if you kept rolling your futures contracts forward for years, you would always be exposed to the 5 Year note's value, but if you bought the underlying 5 Year note, in 2 years it would become AND ACT like a "3 Year note" since it's time to maturity has decreased.
The distinction is important since you'll realize that the futures market is really there to help people exposed to bonds hedge their risk... or others who want exposure to interest rate changes, and who don't want to tie up capital holding the underlying bonds, gain said exposure with minimal margin put up.
I realize this sounds like the absolute basics, but I just wanted to be clear since we are talking about financial futures as a way of pricing out current interest rates and bond prices, and it would be easy for new traders to get these securities mixed up. Heck, I even found a website (semi-popular at that) which misinformed people that the US Government sells and primarily trades Treasury bonds on the CBOT... sigh... so much misinformation online, so I'm just trying to be clear about what's what.
Financial futures are a bond pricing and analysis tool as far as we are concerned, not bonds themselves. (Of course, you are welcome to trade financial futures on their own, no one is stopping you there, but that's not quite what this thread is about..)