The plastic things on the end of shoelaces are called aglets or aiglets. The term originates from the Old French word "aguillette," which is the diminutive form for the word meaning "needle."
Aglets are a simple device with an important function. They prevent the shoelaces from unraveling and becoming hard to thread through the shoe eyelets. Modern aglets are generally made of plastic and formed directly on the shoelace, though in the past they were made of metal that was crimped onto the lace. Plastic aglets are not really a replaceable item. However, in times past, people could visit a shoemaker to have new aglets crimped onto their laces.