Q:

What does "annoy the hell out of somebody" mean?

Source: Embedded Content: Video, Audio, and Canvas

This will play the video on page load, won’t display any controls, and will most likely annoy the hell out of your visitors. Of course you could, if you were kind, put in both the controls and autoplay attributes.

What does "annoy the hell out of somebody" mean? I guess it just means "annoy somebody". I wonder how can that phrase be logically explained?

A:

It's simply idiomatic.

the hell out of
very much:
You scared the hell out of me!
  Note: This may be considered offensive by some people.

So in the OP

... will most likely annoy your visitors very much.

This version is polite. The original is somewhat crude but feels more emphatic. For instance, imagine that you are a visitor to that page and you become very annoyed (pissed, in American slang). If you have no problems swearing (hell is a mild swear), then you might say this page is annoying the hell out of me! [= This is really, really annoying me!].
Note that the meaning the hell out of can differ depending on the context.

—— the hell out of
informal
  Used in verbal phrases to emphasize force, speed, etc.:
'let's get the hell out of here'

This would mean let's leave fast/quickly.
One more example: Dad Trolls The Hell Out Of His Daughter’s Selfies

Here, the meaning is something like dad thoroughly makes fun of his daughter's selfies or dad does a good job of making fun of his daughter's selfies.

