Common starting practices are to open by placing stones on a Hoshi (4-4 point), or close to it, in order to "claim" that corner. As the players are trying to secure as much area as they can, it makes sense to start out in a place that is easily defended, and that is something that's true for corners more than for any other location on the board at the start ...
There are a lot of possibilities for this opening. If you want the bottom space, you could take pincer move(around D) to cooperate with your corner D4; You also could take A to strengthen corner space and threaten to White(this move might better then B due to more threat on White); Take the open up-right corner also OK(corner is more valuable then side); C ...
Capturing territory around the edges of the board is simpler and quicker, because the edge forms a boundary which does not have to be constructed with stones, and which can not be attacked from "outside".
Once a player has a safe territory attached to the edge, it can be extended towards the center of the board.
It is also relevant that a border just three ...
It is plain and simple that it is much easier and more efficient to make life groups and territory in the corners than along the edges or in the centre. In the corner, you need two outer walls, along the edge three, and in the center four to enclose your territory.
And Go is about enclosing territory, after all.
Seems Black has to take the 1-2 vital point to avoid White making 2 eyes. If White begin to deprive Black's liberty from outside, then Black get connected by taking on 1-3 and White deprives outside again. After that, both Black and White have same 3 liberties, but 2 of them are in common used. This becomes seki and it should be the best result for White.
Because you need less stones in the corner to live than in the center. And by extension, you can surround more area in the corner with the same number of stones.
Some figures to visualize this:
Live group in the corner, 6 stones:
Live group in the middle, 10 stones:
(See Smallest Group with Two Eyes on Sensei's ...