The equation at the bottom shows that there is one way of getting two heads, two ways of getting one head and one tail, and one way of getting two tails. N is given by the row in the triangle, and the 'Sum' column shows the number of possible outcomes. The triangle has several other interesting properties. If you count ' x ' numbers in from the edge, it shows you how many ways there are of choosing x items from N items. Two possible outcomes each trial.
Outcomes are exclusive.
Outcomes are independent. Probability of the outcomes remains constant. The frequency distribution of a wide range of natural phenomena approximate the binomial distribution. E.g. Plane crashes, craters on Mercury, release of neurotransmitter at the synapse. Knowing this can be very informative.