What is Reducible representation, totally symmetric representation?

Example 5.5 (The hydrogen orbitals of ammonia)

Take the three $1s$ orbitals of the hydrogens of $\ce{NH3}$ as a basis. $E$ leaves all three in place ($\chi = 3$), $C_3$ moves all three ($\chi = 0$), a $\sigma_v$ leaves one in place and swaps two ($\chi = 1$). With the $C_{3v}$ table: $n_{A_1} = \frac16(3 + 0 + 3\times1) = 1$, $n_{A_2} = \frac16(3 + 0 - 3) = 0$, $n_E = \frac16(6 + 0 + 0) = 1$. So $\Gamma_{\mathrm H} = A_1 + E$: the three hydrogens give one totally symmetric combination and a degenerate pair.