L.O.G. is a tall, thin, imposing figure. He is dressed in modestly simplistic mauve robes and finery. His golden head is in the shape of a Retro Television. The screen that makes up his "face" is green, and stylized to look like a game of Pong, one of the first video games ever created, with his two eyes being the paddles and his long nose being made up of the ball and screen-divider. Climbing all around L.O.G.'s body are small white mechanical mice with plugs for tails.
As L.O.G. has created every video game, he seems all-powerful when in one. Some abilities he's shown to possess include teleportation, the ability to "pause" the game at will (he is unaffected by said pause), and the ability to transform video game characters as he pleases. At one point, he also threatens to reduce Banjo and Kazooie to basic pixels. He uses these magical powers to create several game worlds just for the battle between Banjo, Kazooie and Grunty.
In terms of personality, L.O.G. is both wise and omnipotent, however he often comes off as domineering. He also tries his best to be fair and just, giving Grunty an equal chance of winning as Banjo and Kazooie, despite outwardly siding with the duo.
L.O.G. claims to have had a hand in creating every video game ever made and, being in the position he is in, is occasionally a bit prone to bragging, but generally is a very fair person. He also mentions in passing that he has a wife, a "Lady of Games", who was the first to create games that had "kittens, ponies and ninjas being blown up with rocket launchers".
It is also implied that he was involved in the creation of the earlier games in the Banjo-Kazooie series, being aware of many classic details in the series, including the likes of Tooty and Mumbo's Mountain, which both appeared in Banjo-Kazooie. He references these and other characters and locations in his quiz in the final challenge. An exhibit in Banjoland also directly states that L.O.G. worked hard to get Banjo-Tooie out in a timely manner.
Banjo-Kazooie: Nuts & Bolts