Can someone present a visualization of the partitioning of a $L^p$ space into equivalent classes?

I am a bit confused by what it means for a $L^p$ space to be partitioned into equivalent classes instead of functions.

I understand that give two or more functions $f$, $g$, $h,ldots$ of which are “almost equal” i.e. differs on finite points, then the Lebesgue integral of these functions are identical and $f,g,h$ forms an equivalence class based on the relation “almost equal”

But can someone please sketch a simple picture as to what this partitioning actually look like?

For example.

What would be the entire pink blob called? What would be each of the partition be called? What are elements within each partition?

Thanks!