The first circuit is for \$t\$ (time) \$\le 0\$, and the second is for \$t \ge 0\$.
The book I'm reading says that \$i_L(0^+)=i_L(0^-)\$, but \$i_1(0^-) \neq i_1(0^+)\$ because there are no limitations on the current changing instantaneously at \$t_0\$.
What I don't understand is why \$i_L(0^+)=i_L(0^-)\$, but \$i_1(0^-) \neq i_1(0^+)\$? Wouldn't \$i_L(t)\$ change instantaneously as to whether or not the voltage source would be connected? Why is one instantaneously changeable and not the other?