Nagashime (流し目, lit. "sidelong glance") refers to the way you might look at another person by moving on your eyes without turning your head, or an emotion-filled gaze you might send to your crush.
There's something about eyes that look as if they have more to say—something charming about that mysteriously sexy gaze that draws you in.
Do the sidelong looks below draw you in? Hopefully (or not) like a moth drawn to a flame.