When a product is said to have random widths it means the hardwood planks come in a variety of widths, instead of one standard width. When you purchase a floor like this you will receive boards of all the various widths (you cannot pick and choose which widths you receive). This is a popular choice for those that like the rustic or old-world style.
If a product is said to have random lengths it means the lengths of the hardwood planks vary. This provides a more natural, un-patterned look to the floor when it is installed. Many times random lengths are represented by indicating the range of lengths. For example, “1-7 ft” would mean some of the planks will be 1 ft in length, some will be 7 ft in length, or any length in between.