He's trying to make his audio easier to listen to by using various effects provided by Ardour. The most significant of what he listed is the compressor, which is great for spoken podcasts. It will take any sound that is over a certain threshold and start to to reduce it's volume (eg. compress it), so if he's talking really quietly and then yells something really loud, the person listening isn't subjected to as large of a volume range in their ears.

The limiter just limits the maximum volume, and I'm not sure why he's using an expander.

After comp/limit, a little expander can make the audio less dull sounding.

I'm not sure I understand the point of using an expander after a compressor as one reduces the dynamic range but the other increases it again. What about a little eq cut/boost instead?

There are all sorts of reasons to use an expander after compression/limiting:

https://www.gearslutz.com/board/so-much-gear-so-little-time/...

Sorry I still don't get it. That thread explains some uses for expanders, just not after compressor or limiters in the same effects chain. Surely if you need an expander after a compressor then you've got your setting wrong on the compressor, or maybe you need a noise gate before it.