Concise Bible Dictionary:

The word is from ἐντυγχάνω, which signifies “to meet with, to intercede.” It refers to the intercession of Christ for His saints, while in their present state, to bring them into conformity with the place justifying forgiveness has given them, also to raise them above their trials, and lead them on as priests into the blessed joys and occupations of the sanctuary (Rom. 8:3434Who is he that condemneth? It is Christ that died, yea rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us. (Romans 8:34); Heb. 7:2525Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them. (Hebrews 7:25)). The Holy Spirit also, when they know not what to pray for as they ought, makes intercession for the saints with groanings which cannot be uttered (Rom. 8:26-2726Likewise the Spirit also helpeth our infirmities: for we know not what we should pray for as we ought: but the Spirit itself maketh intercession for us with groanings which cannot be uttered. 27And he that searcheth the hearts knoweth what is the mind of the Spirit, because he maketh intercession for the saints according to the will of God. (Romans 8:26‑27)). In 1 Timothy 2:11I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men; (1 Timothy 2:1) we are instructed to make intercession for all men. It is remarkable that a substantive (ἔντευξις) formed from the above verb is used in 1 Timothy 4:55For it is sanctified by the word of God and prayer. (1 Timothy 4:5), where food is sanctified by the word of God and “prayer,” or, as it there means, reverent communication with Him.

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Ministry Nuggets:

 Full of love to them as the people of God, their rejection of himself does not for a moment suggest the thought to him of giving up his intercession or his testimony for their welfare. Beautiful picture of a heart near the Lord, which, in forgetfulness of self, can love His people as its own! (1 Samuel 12 by J.N. Darby)