In the detailed view of the card, click the card title. It'll show the description and any pages the card is on.
On a dashboard you can hover over the card title and it will display the description as the tool tip.
@user053351 - To my knowledge that's not a possibility out of the box. You could utilize a text card to put on the dashboard and read from the DomoStats or Domo Data Governance datasets to pull the description programatically and display it. You'd need to change the display settings on your existing card to not display the title via your edit dashboard -> [specific card] -> change display settings and uncheck the title box.
Or you just use a text card and put the description in manually.
Short answer is that right now it appears that you can't just display the description like you're want to via the card.