What does the word intercession mean when used in the Bible? What is the biblical definition of intercession?
Intercession is basically the act of interceding between two or more parties. This could include prayers, petitions, or an entreaty requesting the favor of someone. I remember when I was young, two of my friends were about to get into a fight and I tried to intercede on behalf of one of my friends who was being falsely accused by someone else and my other friend was angry at him over this. I interceded on behalf of my one friend’s and told my other friend that this was a false rumor and it was not worth getting into a fight over, so to make intercession is like trying to make peace between two or more parties where there is a natural hostility or dispute. That is the status of every person who has not believed in Jesus. There is hostility between them and God where the wrath of God still abides on them (John 3:36a). That is my definition of intercession, but the biblical definition is what we’ll study next. 
When the nation of Judah was living in great sin, God told Jeremiah “do not pray for this people, or lift up a cry or prayer for them, and do not intercede with me, for I will not hear you” (Jer 7:16). Why would God tell Jeremiah not to pray for Judah? It was because God was about to discipline the nation and send them into captivity for their own good. In other words, God wanted them to be taken captive by Babylon so that they would repent and see their sin and turn again to God. When Eli’s sons were sinning and were derelict in their priestly duties, he said “If someone sins against a man, God will mediate for him, but if someone sins against the Lord, who can intercede for him (1 Sam 2:25)” Obviously no human can intercede between us and God, at least other than Jesus Christ, but Eli’s sons wouldn’t listen to the voice of their father, “for it was the will of the Lord to put them to death” (1 Sam 2:25). Since they didn’t listen to their father’s words, the Lord ended up taking their lives because they took their priestly duties to casually and lightly, and God is too holy to be trifled with (1 Sam 2:34). God is holy and must be regarded as holy.
The Spirit’s Intercession
Sometimes when I am praying, I may not even know how to put it into words, but the Spirit does and He helps me just as Paul writes about in Romans 8:26, writing, “Likewise the Spirit helps us in our weakness. For we do not know what to pray for as we ought, but the Spirit himself intercedes for us with groanings too deep for words,” and so the Holy Spirit “searches hearts [and] knows what is the mind of the Spirit, because the Spirit intercedes for the saints according to the will of God” (Rom 8:27). Ever felt at a loss for words? I have. If you’re searching for the right words to pray to God but can’t find them, the Holy Spirit can help you, so yield to Him and pray through Jesus Christ to the Father. The Holy Spirit intercedes on our behalf, even to the point of helping us pray, even if “we do not know what to pray for as we ought.”
The Prophets Intercession
Jeremiah wrote that “If they are prophets, and if the word of the Lord is with them, then let them intercede with the Lord of hosts, that the vessels that are left in the house of the Lord, in the house of the king of Judah, and in Jerusalem may not go to Babylon” (Jer 27:18), so there was hope for those left in Judah after the captivity of most of the nation, but it would only be if the prophets interceded on their behalf and the repented of their sins. Here the word intercession means to pray in behalf of others, and in this case, a prayer can be intercessory prayer. Here we read that Jeremiah was praying for the remnant of Judah that was left behind by the Babylonians who took most of the nation of Judah captive, yet God left a remnant in Jerusalem that He would use to keep the nation alive. Many times, the prophets were a mouthpiece for God, speaking on behalf of God, but most of those times, the people ignored the prophets, and as a result, calamity and captivity followed. By then, no amount of intercession would help.
Paul requested “that supplications, prayers, intercessions, and thanksgivings be made for all people” (1 Tim 2:1), but there is another One Who intercedes on our behalf before the Father, and it is Jesus Christ, and “Consequently, he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them” (Heb 7:25). Today, Jesus is still at the right hand of the Father, interceding on our behalf. That’s why we pray in Jesus’ name. Jesus Christ has access to the Father, and Jesus Christ, Who is also God, was prophesied about long ago by Isaiah the Prophet who wrote, “Therefore I will divide him a portion with the many, and he shall divide the spoil with the strong, because he poured out his soul to death and was numbered with the transgressors; yet he bore the sin of many, and makes intercession for the transgressors” (Isaiah 53:12). If not for Jesus standing between us and a holy God, we would have no hope of reconciliation for our sins because they had separated us from His Holiness (Isaiah 59:2), but thankfully, Jesus “always lives to make intercession” for us.
Jesus’ atoning death at Calvary bridged the gap that only the cross of Christ could bridge (Acts 4:12). If not for His sinless life, death, and resurrection, we’d still have the wrath of God abiding on us (John 3:36b) and would die in our sins, and we’d have nothing but a hopeless, Christ-less eternity ahead of us (Rev 20:12-15), so I plead with you to put your trust in Him and He will intercede on your behalf, and on behalf of all who repent and believe in Him (John 3:16).
Here is some related reading for you: How Does God Use Intercession for Good or Bad? 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible: English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.