Talking head
From RWP Wiki
Talking heads (also called mumbles, after the noises they make) are a stylized approach to dialog in the Banjo-Kazooie series. When characters converse in the Banjo-Kazooie games, two text boxes appear at the top and bottom of the screen, each containing an animated head of those conversing. The top box has the talking head on the right, and is generally reserved for the player's character. The bottom contains the head of any characters they are talking to, usally NPCs, which are on the right side. When switching between characters (I.E., from Banjo to Kazooie), the respective talking head simply fades away to reveal the person who is talking next. When the heads talk, they make a short animation showing it and make repeated noises specific to the character (Banjo's, for example, makes "Huh-huh-huh-huh" noises).
The reason for the talking head style likely comes from the Nintendo 64's use of cartridges, and the limited space available on them. In 1998, it would possibly have been too expensive and inefficient to produce a cartridge large enough to contain full voice acting (though Nintendo's Star Fox 64 in 1997 and even Rare's own Conker's Bad Fur Day in 2001 contained full voice acting), and rather than opt for regular text boxes, ala Nintendo's Zelda games, they decided on a fairly unique style that relied on text but still gave each character their own voice.
However, due to their prominence, they return in Banjo-Kazooie: Nuts & Bolts, despite being on the Xbox 360, which could easily support full voice acting. Rare stated in Scribes that it took them a while to decide which route to take for dialog in the new game, but finally they decided on the classic "last-gen" style. However, a change made in the game is that, rather than the pre-rendered sprites used in the original games, Nuts & Bolts uses in-game models of the characters' faces for the talking heads.