Savor is the American spelling of British savour; the meaning is the same. As a verb, it means to enjoy something slowly with your senses — most often a taste, but also a moment you do not want to rush. You do not gulp the soup; you stay with it. “She savored the last day of the trip” stretches the same idea from the mouth to time. As a noun, a savor is a taste or smell, often a pleasant one, though that noun now feels a bit literary; most people just say taste or flavor. In the US you write savor and savory; in the UK, savour and savoury. Though actually there is a sister-word tangle here: the adjective savory / savoury also means “salty or spicy, not sweet,” as in a savory pie. That is the same family, not a different spelling of the verb, and it is the sense students meet on menus.