Understanding why a portfolio can be diversified and still fall sharply

My portfolio owns broad funds across many companies and countries, yet during the recent downturn nearly everything on the screen fell together. I thought diversification meant the pieces would offset one another more often. I now realize it mainly reduces the risk of any one company ruining the plan, not the risk of the entire stock market having a rough year. How do you explain the difference between diversifying within stocks and holding assets that respond differently to economic shocks?