The simplest definition of importunity is persistent and urgent asking.  Importune prayer then is persistent and urgent; it is prayer that pleads with God and asks Him repeatedly for the things we need.           

This kind of praying may seem selfish and perhaps childish, but it really isn’t because it is prayer in the will of God and is usually for others instead of self.  In fact, the source of this kind of prayer is right from the heart of God.  It is how the Holy Spirit pleads and prays for us (Rom. 8:26).  It is how God persistently and urgently seeks us out, speaks to us, and constantly seeks to help us and love us (Jer. 31:3, Jn. 6:44).  Thus, when I pray with importunity, I pray for myself and for others the same way and with the same heart as the Holy Spirit does.  I follow after His prayers. …