Intercessory prayer is praying/interceding on behalf of others
We are to intercede for others
1 Tim 2:1-8 First of all, then, I urge that entreaties and prayers, petitions and thanksgivings, be made on behalf of all men, 2 for kings and all who are in authority, so that we may lead a tranquil and quiet life in all godliness and dignity. 3 This is good and acceptable in the sight of God our Savior, 4 who desires all men to be saved and to come to the knowledge of the truth. 5 For there is one God, and one mediator also between God and men, the man Christ Jesus, 6 who gave Himself as a ransom for all, the testimony given at the proper time. 7 For this I was appointed a preacher and an apostle (I am telling the truth, I am not lying) as a teacher of the Gentiles in faith and truth.
8 Therefore I want the men in every place to pray, lifting up holy hands, without wrath and dissension.