When you paste a link to another Trello Card at some card's description, Websites for Trello will, in the process of rendering the page, convert that link to a link that leads to the actual rendered version of the linked card. This enables easy linking between posts without you having to search for the URLs each card will be assigned in the rendered website (which are, also, terribly susceptible to change).
So, for example, a link that is written, in the source of this same card (https://trello.com/c/8EhEUiva/17-links-to-other-cards) as:
[Go to the documentation home](/c/pUtKmWqW)
becomes the following link: