A Life Link (ライフリンク Raifu Rinku), simply put, is a link between two people in that if one person dies, they will be brought back to life, so long as the other person continues to live. If both people are killed in the same time frame, neither comes back to life.
Noel Vermillion formed a life-link with Hazama at some unknown point. Ragna the Bloodedge also shares a life link with Nu -No. 13-. A life link in top form, according to Terumi, should make the two people stronger, as he comments on how Noel was not able to beat Taokaka in her story mode.