There are two kinds of video AirPlay: ‘basic’ AirPlay of just the video file, and Screen Mirroring.
‘Basic’ AirPlay is very efficient as it passes just the video undecoded to the Apple TV. It also blocks the video on the ‘source’ device. This feature is supported by some Apple software apps: iTunes, QuickTime Player, Safari.
Screen Mirroring on the other hand does what it says, it mirrors the screen, but it has to compress what happens on screen into a live video stream. This live encoding asks a lot of the source machine’s graphics chip and the network, when a lot is happening on screen. Modern/faster notebooks will have it easier doing this than the earlier generation. This feature is supported by nearly all apps (except those that don’t allow screen recording).
AirPlay send video and audio together, so they should stay in sync.
If the sending computer is doing much other stuff in the background, then you may notice less frames-per-second for AirPlay. It is not a solution for gaming, because of the lag (one or two seconds worth of buffering) and the demand on the graphics chip.
AirPlay is limited to HD (1920×1080), so higher resolutions will be reduced on-the-fly.