Question

what is the bond order of oxygen and what is the reason behind it?

Answer 1

Two. The reason is that this is the lowest energy configuration of the electrons when you have two oxygen nuclei near each other. That is the fundamental "why," but there are various ways in which it is stated, so that you can generalize to other molecules.

One of the most common, in introductory chemistry class, is to invoke Gilbert Lewis's idea that chemical bonds are made by the sharing of pairs of valence electrons, and that the most stable arrangement of electrons is the one where each nucleus can be assigned 4 pairs of electrons, shared or not.

An oxygen atom has 6 valence electrons. If we have two of them, we have 6 pairs. How can we assign pairs so that each oxygen nucleus has 4? Only by assigning 2 pairs to be shared -- so BOTH oxygens get to list them -- and assigning the other 4 pairs to be unshared (also called "lone pairs.") Thus for each oxygen nucleus we have:

unshared pairs: 2
shared pairs: 2
----------------
total: 4

And all is good. This is useful because we can extend it to other molecules. For example, what if we had two nitrogen atoms? Each nitrogen comes with 5 valence electrons, so with two we have 5 pairs. Now we can only have 4 pairs assigned to each nitrogen nucleus if we let 3 be shared:

unshared pairs: 1
shared pairs: 3
---------------
total: 4

So we can predict N2 has a bond order of 3, also called a triple bond.

One important exception is the hydrogen nucleus, which can only accomodate two electrons, so we always want to assign 1 (shared) pair to a hydrogen nucleus.

It all breaks down a little in Period 3 and below, because atoms there can and often do accomodate more than 4 pairs of electrons near them.