The in-game announcer is a non-character voice that lets the players know what is occurring in the game. This is different from a voiceover, which may be attached to a character to relate story-driven events.
You'll commonly hear this voice in first-person shooters. This is the voice that announces game modes in a game like Halo (The voice that says 'Slayer' or 'Capture the Flag' at the start of a match), as well as calls out when game conditions have changed (such as 'You have gained the lead', 'Flag captured', or 'Game over'). The most iconic use of this voice is to declare when people gain consecutive kills in a row in competitive modes, such as 'Double kill!' or 'Triple kill!'.
This announcer voice is also prevalent in real-time strategy games, though usually it is tied to some kind of iconic assistant non-unit. As an example, in the game Starcraft, if you are playing the Terran faction, alerts as to the status of the game are called out by the robotic AI adjutant. This isn't a unit you can control, but merely a thematic representation of the fact that the player is treated as a commander, so these non-units are your support crew. These may be messages such as 'Our allies are under attack', or 'Our base is under attack'. In the single-player missions within Starcraft 2, you'll commonly hear this voice relate mission objectives to you as a player.
In the Bejeweled series, the announcer will give the player comments on how well they did during the game with praising messages like 'Excellent' and 'Spectacular'. It also tells the player how much time remains in various modes like '3 Minutes' in Bejeweled Twist, and 'Time Up" from Bejeweled 3.