Live commentary or narration is one of two subsets of narration used in Video Let's Plays, as opposed to post commentary. Live commentary refers to narration which is recorded by the player(s) as the game is being played.
Advantages and Disadvantages vs Post Commentary
Live commentary tends to be preferred in the LP community over post commentary for a number of reasons. These may include capturing the player's natural reactions to occurences in the game, such as surprise during plot twists or frustration with failure, as well as some added humour in some situations.
However, recording commentary live is a skill which can be hard to master at first. Being able to talk and play the game competently at the same time requires practice, particularly if the player wants to make note of certain aspects of the game as they concentrate on playing. Some Let's Players will make notes before they start recording to help remember to mention certain things in these situations. Otherwise, post commentary is an option if a high level of concentration is required to play the game well.
For highly informative LPs, post commentary is preferred as it allows the LPer to provide more detail and to tailor the information more accurately to what is being shown on the screen, without risk of having to cut one's self off in mid-sentence. Additionally, in some particularly action packed videos, the LPer may not be able to notice everything that is happening with live commentary. Post commentary allows for greater detail in analysis -- this is especially useful for certain real-time strategy games, and flight simulators.