This string has various pattern effects, and to do that it takes advantage of inherent properties of diodes (light-emitting or not) and human vision. Each bulb in the string is wired in opposite polarity from the one that precedes it, so any effect that alternates half of the string will light, because a diode wired against the flow of current will simply block the current.
When the string appears to be fully lit, it takes advantage of the slow decay of impulses in the human retina - it rapidly alternates the current, lighting each half of the string in succession. If the string and the observer remain stationary, the entire string appears to be lit. Moving the observer or the string might result in some flicker being observed.