"Intercession" is exactly the same Greek word as is translated "prayer" in I Timothy 4:5. It has an interesting etymology that instructs us on an important aspect of prayer. The word, a verb, is entugchanein.
It began to appear in Greek centuries before Christ, meaning simply "to meet a person," as if a person would meet another along the way. However, through the centuries, the word took on a somewhat different meaning. Eventually, it meant, not just "to meet," but "to meet and converse." This is natural because, if a person falls in with another along the way, he usually does not ignore the other but strikes up a conversation.
Then, as time went by, it began to take on yet a different meaning: "to have intimate fellowship with the person." To this point, the word describes how to have a right approach to God. In practical fact, it illustrates that we are not conversing with God from a distance. We are so intimately associated with Him that we are His children. This word is describing an intimate family relationship. God is not way off on the top of a mountain somewhere. Even as early as Deuteronomy 30:14, He says, "The word is very near you, in your mouth and in your heart"!
If we are going to have the right kind of fellowship and relationship with God in prayer, we have to understand that we are in His very presence. Looking at this humanly and physically, this is how He can rub off on us. We are in His fellowship, in His presence. He is not far off. When Christ gave His life for us, the veil of the Temple was torn from top to bottom, symbolizing that access to God was completely open to Him, and now we have this same access to the Father through Christ. We are right before His throne when we are talking to Him.
However, entugchanein continued to change. The change shows up in the noun form of the word, enteuxis, meaning "a petition to a king." It can be used in the sense of the king summoning someone into his presence or of someone presenting a request to the king. Putting these together, it suggests that we have "intimate access to petition the king." We do not have intimate fellowship with just anybody, but to the King of all the universe!
We have both privilege and power in prayer. This is where the concept "the power of prayer" comes from. Because we have the privilege to come before the King in intimate fellowship, we have access to His power. It is not that prayer itself has the power, but that we have access to the One who has the power.
This means we have to be extra careful what we ask God: He may give us what we ask, and we will be sorry. Mighty forces can be unleashed when we ask God for things. God's people have a responsibility to ask of Him things that are according to His will.
As a tool, prayer is to be used to accomplish a wide variety of things within God's purpose. It is to be used in regard to the things of this life. God wants us to pray about this life, as in supplying our daily need. However, He will primarily use it, not for this life, but for His eternal purpose, reproducing Himself and creating His holiness in us. His purpose is in preparing us for the Kingdom of God.
So be warned that His purpose will supersede ours when we pray.