Below is an extract from Octavius Winslow's Book, No Condemnation, describing what is meant in Romans 8:26 in the interceding work of the Holy Spirit. Click here to read the whole chapter on v. 26
"We know not what we should pray for as we ought; but the Spirit itself makes intercession for us with groanings which cannot be uttered." The Holy Spirit is here represented in the character of a pleader, or advocate for the saints. To form a vivid conception of this truth, we have but to imagine an anxious and embarrassed client prosecuting some important suit, or, perchance, battling for his life in a court of justice. At his side stands his counselor, thoroughly acquainted with the nature of his case, and deeply versed in the bearings of the law. He is there to instruct the suppliant how to shape his course, with what arguments to support, with what pleas to urge, with what words to clothe his suit. Such is the advocacy and such the aid of the Spirit in the matter of prayer. We stand in the presence of the Lord- it may be to deprecate a deserved punishment, or to plead for a needed blessing. "We know not what we should pray for as we ought." How shall we order our cause before the Great Judge? With what feelings, with what language, with what arguments shall we unburden our heart, unveil our sorrow, confess our sin, and make known our request? How overcome the remembrance of past ingratitude, and the conviction of present guilt, and the pressure of deep neediness, and the overwhelming sense of the Divine Majesty? How wake the heart to feeling, how rouse the dull, sluggish emotions of the soul, how recall the truant affections, and how concentrate the mind upon the holy and awesome engagement? But our Counselor is there!"The Spirit itself makes intercession for us." And how does he this? He indites the prayer. Think not that that spiritual petition which breathed from your lips and rose as an incense-cloud before the mercy-seat was other than the inditing of the Holy Spirit. He inspired that prayer, he created those desires, and he awoke those groanings. The form of your petition may have been ungraceful- your language simple, your sentences broken, your accents tremulous, yet was there an eloquence and a power in that prayer which reached the heart and moved the arm of God. It overcame the Angel of the Covenant. And whose eloquence and whose power was it? The interceding Spirit. He also teaches us what to pray for. Many and urgent as our needs are, we only accurately know them as the Spirit makes them known. Alas, what profound ignorance of ourselves must we cherish when we know not what we should ask God for as we ought! But the Spirit reveals our deep necessity, convinces us of our emptiness, poverty, and need, and teaches us what blessings to ask, what evils to deprecate, what mercies to implore.