To lengthen is to make something longer, either physically or in time. During the spring and early summer, the days lengthen, as sundown comes later and later.
Mascara lengthens your eyelashes, and letting out your hem lengthens your jeans. As time goes by, your years of experience lengthen, and if you don't cut your hair or trim your beard, those lengthen as well. Lengthen dates from the 14th century — earlier, the verb was length, from a Germanic root that's also the basis of "long."