You can think of a vector like a right angle triangle.
The x and y components are the lengths of the two shorter sides which are at right angles to eachother. The length (a) is the hypotenuse which joins the start of one component and the end of the other together.
You can use pythagoras' theorem to calculate the length of the hypotenuse.
For the (0,1) vector |a| = sqrt(1^2 + 0^2) = sqrt(1) = 1
So the length is 1
For the (1,1) vector |a| = sqrt(1^2 + 1^2) = sqrt(1 + 1) = sqrt(2)
So the lengt is sqrt(2) or about 1.41