Noninverting Amplifier
\$ v_{in} \$ is the non-inverting input.  \$ v_1 \$ is the inverting input.  \$ v_{i}\$ is the voltage difference between the inverting and non-inverting input.  It's drawn between the inputs of the OpAmp.  That's how the book have defined it for the purposes of discussion.  Thus \$ v_i = v_{in} - v_1 \$.

p.s. Naming the three variables \$ v_i \$, \$ v_{in} \$, \$ v_1 \$ is just begging for dyslexic errors.