The player is depicted as a character on-screen performing at a public bar. The words to the song scroll bottom to top at the bottom of the screen, above a piano roll representation of the relative pitches at which they are to be sung (the game calls these "note tubes"). At the left end of this area, a "pitch star" shows the pitch which the player is singing and provides feedback on whether (s)he's hitting the notes. A "crowd meter" shows the mood of the crowd as the player sings; if s/he does a good job of hitting notes on-pitch then the crowd will cheer more loudly and clap in rhythm with the song, and the scene will become more vividly animated. If the crowd meter falls all the way to the lowest rating, the audience will boo the character off-stage and the game is over.
Each song is divided into approximately 30 to 50 "phrases". A meter will fill up and turn from red to green for each phrase, based on how well the player sings the right notes; if the player can fill the meter to green, (s)he will score more points, and getting several greens in a row will create a "combo" and award a 2x score multiplier until the player fails to make green on another phrase. This blue meter resembles how long you should hold the note for and at what pitch. The game can be set at higher difficulties which make this meter larger and require the player to hit the right notes more precisely to fill it to green.
Source: Wikipedia, "Karaoke revolution", available under the CC-BY-SA License.