How floats work
When floating elements exist on the page, non-floating elements wrap around the floating elements, similar to how text goes around a picture in a newspaper. From a document perspective (the original purpose of HTML), this is how floats work.
float vs display:inline
Before the invention of display:inline-block, websites use float to set elements beside each other. float is preferred over display:inline since with the latter, you can't set the element's dimensions (width and height) as well as vertical paddings (top and bottom) - which floated elements can do since they're treated as block elements.
Float problems
The main problem is that we're using float against its intended purpose.
Another is that while float allows side-by-side block-level elements, floats do not impart shape to its container. It's like position:absolute, where the element is "taken out of the layout". For instance, when an empty container contains a floating 100px x 100px <div>, the <div> will not impart 100px in height to the container.
Unlike position:absolute, it affects the content that surrounds it. Content after the floated element will "wrap" around the element. It starts by rendering beside it and then below it, like how newspaper text would flow around an image.
Clearfix to the rescue
What clearfix does is to force content after the floats or the container containing the floats to render below it. There are a lot of versions for clear-fix, but it got its name from the version that's commonly being used - the one that uses the CSS property clear.
Examples
Here are several ways to do clearfix , depending on the browser and use case. One only needs to know how to use the clear property in CSS and how floats render in each browser in order to achieve a perfect cross-browser clear-fix.
What you have
Your provided style is a form of clearfix with backwards compatibility. I found an article about this clearfix. It turns out, it's an OLD clearfix - still catering the old browsers. There is a newer, cleaner version of it in the article also. Here's the breakdown:
The first clearfix you have appends an invisible pseudo-element, which is styled clear:both, between the target element and the next element. This forces the pseudo-element to render below the target, and the next element below the pseudo-element.
The second one appends the style display:inline-block which is not supported by earlier browsers. inline-block is like inline but gives you some properties that block elements, like width, height as well as vertical padding. This was targeted for IE-MAC.
This was the reapplication of display:block due to IE-MAC rule above. This rule was "hidden" from IE-MAC.
All in all, these 3 rules keep the .clearfix working cross-browser, with old browsers in mind.
