What are linear pair of angles?

When the two adjacent angles are supplementary, such pairs of angles are known as linear pairs.

In other words, a linear pair is a pair of adjacent angles whose non-common sides are rays pointing in the opposite direction.

In the above figure, ∠AOB and ∠BOC are supplementary angles which means, 

∠AOB + ∠BOC = 180° 

And these two are adjacent angles too because they have a common vertex O and a common side OB.

∠AOB and ∠BOC are supplementary as well as adjacent angles, so they are a linear pair.