A yield curve is a graphical representation of yields on bonds with different maturities. The most common example is the government bond yield curve, but it is very well possible to render a yield curve for other types of bonds, such as corporate bonds, high yield bonds, etc.
The government bond yield curve is often referred to as the benchmark yield curve; the image above shows this curve for US government bonds on 1 November 2019. Data to draw a yield curve (for US gov bonds) are readily available from various sources. A good source to check yields for various maturities of government bonds is the website of the US Department of the treasury (www.treasury.gov). The image above is rendered using data from that source.
In a normal situation, one would expect to receive a higher compensation (yield) for longer maturities. When you lend money to the government for 20 or 30 years, it intuitively makes sense to receive a higher compensation than when you lend it only for a year or a few months.
As these yields change every day, the shape of the curve will change accordingly. Because financial markets have a tendency of throwing curve balls from time to time, unusual/unintuitive situations can and will happen.
A normal-shaped yield curve is usually seen in an economic environment that shows normal growth and little-to-no changes in inflation or available credit.
An inverted curve is usually seen as a signal that economic growth will soon stabilize or reverse, maybe even signaling the start of a recession. This is caused by investors thinking that the period of economic growth is or will soon be over, making them more likely to accept lower rates before they fall even further. This process can cause (partial) yield curve inversions.
An inverted yield curve does not have to be "completely" inverted as in the image. Sometimes only part(s) of the curve are inverted; this can cause humps or dents in the curve as we would expect it to be shaped.
It is not so much the current shape of the curve that can help us to solve the financial puzzle, but more the transition and the changing of the shape of the curve that will provide us with clues for the potential future direction of the economy.
As with many graphs/tools/relationships/etc. that we use in our analysis, the yield curve will not provide us with the definitive answer. Like all other tools that we have at our disposal, it is just a piece of the puzzle that we are trying to solve every day.