Youth is the opposite of elderly. When something is new, it can be called young. Sometimes "young" is only for living things, and things that are not alive are "new". The word youth is mostly used to describe young people between the puberty and adulthood (though some would include young adulthood up to age 39, as part of the definition of being young) Old can refer to someone or something's age. Young can mean that something is current to date or well before its "best by" date.
Different things lose their youth or grow old at different rates. For example, some machines are only be considered young for roughly one year. There are laws about the age of majority when young people are legally treated as adults. Even after that age, young people may still be seen as immature. This is because mental and emotional development isn't done until around age 25, and because many young people have not yet had adult life experiences.
For some people, youth is an obsession. They want to look young. Because of this, they use various products like face cream and plastic surgery, to stop or slow their looking older. The "Fountain of Youth" was a popular myth, and people thought that if you took water from the fountain, you would never be old. Now however, we know that this was a myth, and it was not magical at all.