What is the redness on the the lower part of my legs of some elderly folks?

Can be poor veins. A common change as people get older is for the blood vessels in the legs to get weaker and often damaged. Poor vein function (varicose veins, venous insufficiency) can cause swelling, and blood pooling. Gravity makes it worse. Sometimes vessels leak blood which can make the skin look red or brownish. Prevent weak veins by staying active, stretching the legs, and putting them up when sitting.