A train is a rail vehicle. It is usually made up of a large number of carriages that carry either people or goods, and one or more engines that pull it along the rails.
Someone is vain if they are overly interested in their own appearance, achievements or other things about themselves.
Vain is also another word for futile, as in "I tried in vain".
Something is waning when it is decreasing in size, intensity, strength or power. For example, "his health was waning".
The picture is of the waning moon. The opposite of waning is waxing.