Dude read this,
It will help you a lot.
https://www.qsl.net/n1bwt/chap1.pdf
Directionality is how strong is the gain at that particular point. It depends on type of antenna, such as handphone of course you don want directionality because you want the handphone antenna to receive signals from different directions.
Basically, directionality means your gain intensity. If you see your gain pointing aggresively at one direction, that means the directionality of the antenna is of that direction, but if you don't see any gain pointing anywhere or rather scattered around the region...that means is not a directional type of antenna.
Read the link, i given you. It will increase your understanding 100 times more.
---------- Post added at 20:04 ---------- Previous post was at 19:44 ----------
On your second image...
The E-plane is the red color that shaped like a peanut.
The H-plane is the green color omnidirection pattern (omnidirection means that it's circular all around).