Bonds are a vast topic and underappreciated, I'm far from an expert, I haven't been watching bond markets closely until the past 1-2 years when I learned just how profitable they can be and how important they are to the economy. The bond market is vastly larger than the stock market as a whole.
There are all different kind of bonds but for now let's talk about US government bonds. Not long ago you could get a 2.5% return on the 10 year note, but with the downward pressure on rates this is now down to 1.5% or so. Naturally when you have a bond returning 2.5% while newer bonds are returning 1.5% your bond is more valuable and more in demand compared to the newer bonds thus its value goes up in direct proportion to the higher yield yours is priced at. So lower yields raise bond values.
Inversely, if rates were to rise back to 5%, the old bonds you are holding at 2.5% are now less valuable than ones yielding 5% thus if you want to sell your lower yielding bonds you would have to cut the price to get someone to buy it, making bond price go down with higher yields.
Yields are subject to the FED funds rate, as well market pressures. People rushing to buy bonds like they are now puts upward pressure on bond prices and downward pressures on yields. So many more people are rushing to buy 10 year notes compared to 2 year notes that the yield of the 10 year note is now LOWER than the yield of a 2 year note (inversion), which is obviously not normal and signals significant problems ahead.
Bonds are typically looked at as boring and for older people, but the 20 year note has actually outperformed the S&P over the past year (check TLT vs SPY)