I found a very useful illustration of the operations here
As I understand,
after the line:
vec.set( ( event.clientX / window.innerWidth ) * 2 - 1, - ( event.clientY / window.innerHeight ) * 2 + 1, 0.5 );
vec is the position of a 3D point (pointA) in space along the ray in Normalized Device Coordinates
after the line:
vec.unproject( camera );
vec is the position of pointA in 3D space in world coordinates
after the line:
vec.sub( camera.position ).normalize();
vec is the normalized ray direction from the camera
after the line:
var distance = ( targetZ - camera.position.z ) / vec.z;
distance is the distance/scale by which to travel along the ray, until reaching a point on the ray which lies in plane z=targetZ
after the line:
pos.copy( camera.position ).add( vec.multiplyScalar( distance ) );
pos is the position of the 3D point (pointB) which lies on the ray and is at z==targetZ