The manual suggests to examine the pixels by 2-by-2 neighbours. These neighbours can take 6 different patterns which I tried to picture here. Examining each and every 2-by-2 neighbour and calculating the total is how bwarea works.

You are mixing 2 of the variables. in the documentation we can see the following:

BW2 = bwareaopen(BW, P)
BW2 = bwareaopen(BW, P, conn)

Where you have P and conn variables.

conn is the neighbourhood variable. With this you chose with values you understand as "neigbour". See example:

conn=4;

- X -
X 0 X
- X - 

conn=8

X X X
X 0 X
X X X

Higher numbers are for higher dimensions. but the P variable is the variable to choose what is "small". The function bwareaopen will delete white areas smaller than P pixels.

In the example in the documentation you can see:

    BW = imread('text.png');
    BW2 = bwareaopen(BW, 50);
    imshow(BW);

But that "50" is the P variable, not conn. as conn is not defined it will be set as default, in this case 8.

bwareaopen() removes white areas with size less than p. If you want to remvove the black holes inside your white areas you should use the function imfill() .

Edit: Alternativly, you could use the bwareaopen() function on the inverse image, i.e. on 1-Im