"X-UA-Compatible" content="IE=9; IE=8; IE=7; IE=EDGE"

Question

If you support IE, for versions of Internet Explorer 8 and above, this:

<meta http-equiv="X-UA-Compatible" content="IE=9; IE=8; IE=7" />

Forces the browser to render as that particular version's standards. It is not supported for IE7 and below.

If you separate with semi-colon, it sets compatibility levels for different versions. For example:

<meta http-equiv="X-UA-Compatible" content="IE=7; IE=9" />

Renders IE7 and IE8 as IE7, but IE9 as IE9. It allows for different levels of backwards compatibility. In real life, though, you should only chose one of the options:

<meta http-equiv="X-UA-Compatible" content="IE=8" />

This allows for much easier testing and maintenance. Although generally the more useful version of this is using Emulate:

<meta http-equiv="X-UA-Compatible" content="IE=EmulateIE8" />

For this:

<meta http-equiv="X-UA-Compatible" content="IE=Edge" />

It forces the browser the render at whatever the most recent version's standards are.

For more information, there is plenty to read about on MSDN,

In certain cases, it might be necessary to restrict the display of a webpage to a document mode supported by an earlier version of Internet Explorer. You can do this by serving the page with an x-ua-compatible header. For more info, see Specifying legacy document modes.
- https://msdn.microsoft.com/library/cc288325

Thus this tag is used to future proof the webpage, such that the older / compatible engine is used to render it the same way as intended by the creator.

Make sure that you have checked it to work properly with the IE version you specify.