It helps to separate two yield measures that get blurred together. The current yield is a security's annual interest divided by its current market price, a simple snapshot: the SEC's investor materials give the example of a bond with a $1,000 market price paying $80 a year having an 8 percent current yield. The yield to maturity is the more complete figure, the total return an investor earns if the security is held to maturity, counting every interest payment and the difference between the purchase price and the face value repaid at the end. Yield to maturity is a projection rather than a promise, because it assumes interest can be reinvested at the same rate, which may not hold; still, it is the number most often meant by "the yield" on a longer security.
The yield curve is the second half of the subject. It is a plot of Treasury yields against their maturities at a single moment, from the shortest bills to the 30-year bond. The U.S. Treasury constructs and publishes a daily par yield curve from market quotes on the most recently auctioned securities at each maturity. In a normal curve, longer maturities yield more than shorter ones, compensating investors for tying up money longer and for the greater price sensitivity of long bonds. When that ordering reverses, so that shorter-term yields exceed longer-term ones, the curve is described as inverted.
An inverted yield curve draws attention because of its record as a recession indicator, but the claim has to be stated carefully. The Federal Reserve Bank of New York's research, which pioneered using the curve as a leading indicator, measures the "term spread" as the difference between the 10-year and 3-month Treasury rates and notes that since 1960 an inversion on that measure has preceded every U.S. recession on record. It also cautions that different spreads behave differently, that the 10-year-minus-2-year spread may invert earlier than the 10-year-minus-3-month spread, and that the level of the spread, sustained over time, forecasts better than a brief one-day move. In other words, a claim that "the yield curve inverted" is incomplete without saying which spread, and a single day's inversion means less than one that persists. The curve is a genuinely useful signal, not an infallible one: it has produced a false alarm, and the lead time between an inversion and any downturn has been long and variable.
For a household, Treasury yields matter even for people who own no Treasuries. They set the floor under other interest rates: mortgage rates, corporate bond yields, and the rates on savings vehicles all take their cue from where Treasury yields sit, and rising yields also change how investors value stocks, since a higher risk-free return raises the bar every other investment is compared against. Watching Treasury yields is, in effect, watching the price of safe money, which ripples through nearly every other financial decision.