The phrase "to elongate the spine" means to stretch or lengthen your spine, creating a taller and more upright posture. It involves straightening your back and gently pulling your head upward to align your spine. Full definition
Instead of practicing at a fast clip, in which it may be possible to forget about alignment and breath, Reif suggests that you hold each pose for several breaths: «Take the time to make sure you are elongating your spine as much as you can in a pose and breathing diaphragmatically.» (yogainternational.com)
This pose will increase your stamina, improve flexibility of the torso, strengthen the ankles, feet and legs, while elongating the spine and opening the hips. (mindbodygreen.com)
It seemed like it might be the larva of a sea bass, but it was unique in having seven elongated spines sticking out from its back. (sciencemag.org)