Liking things gives you the chance to share your musical tastes. You can give a Thumbs-Up to indicate a Like or you can Like an artist, song or album anywhere on Pandora.

You can like a track without giving it a Thumbs-up. To do so, click on the name of the track, then click on 'Like this track.'

On the Web:

Likes are displayed under My Profile and Music Feed. Anyone who's following you on Pandora can see your likes.
 
On the iPhone and iPod:

To view your Likes on your iPhone or iPod Touch, first open the Pandora app and go to the Station list. At the bottom of this screen select 'Profile' and then tap on 'Likes.'
 
On and Android:

From the Now Playing screen touch the back arrow in the upper left (near the Pandora icon). Then select the Profile tab. 

When you select Likes, you will then have the option to see your list of Liked Tracks, Artists or Albums. You can even listen to samples of individual tracks. 

At the top of the next screen, you can specify whether you would like to see a list of your liked tracks, artists or albums.