My Mom used to tell me this to encourage me to eat my spinach…which I hated! But dear old Mom was wrong. Spinach indeed contains a lot of iron, but almost all of the iron is in a form that your body cannot use, and it just passes right through you. Popeye was a fraud it seems!
Dietary iron comes in two forms. Heme iron, which is found only in animal products—meat, poultry, and seafood. Then there is non-heme iron which is found in many plants. Your body readily absorbs heme iron and can use it for making red blood cells and other needs. Non-heme iron, in contrast, is very poorly absorbed so the body cannot use it. To make things worse, spinach contains a lot of oxalic acid, which further inhibits iron absorption. So sorry Mom, I am not going to eat the spinach!
Because heme iron is found only in animal flesh, vegetarians/vegans often suffer from iron deficiency anemia. With careful diet planning and/or supplements this can be avoided.