It's prayer enabled and shaped by the Holy Spirit rather than religious performance or self-reliance. It includes ordinary prayer offered from your union with Christ, and for some believers it includes tongues. And when you don't know how to pray, the Spirit Himself helps and intercedes for you.
The Grace Answer
"Praying in the Spirit" sounds mysterious, and it sometimes gets treated as an elite level only certain Christians reach. Scripture describes it more simply and more kindly. At its heart it means prayer that is enabled, animated, and shaped by the Holy Spirit, rather than prayer driven by the flesh or by mechanical religious performance. That is why Jude can tell ordinary believers to be “praying in the Holy Spirit,” and Paul can urge the whole church to be “praying always with all prayer and supplication in the Spirit.” It is not a badge for the advanced. Every believer has the Spirit, and every believer may pray with His help.
Within that, Scripture also describes prayer that runs past the edge of your own words. Paul writes, “if I pray in a tongue, my spirit prays, but my understanding is unfruitful,” and concludes, “I will pray with the spirit, and I will also pray with the understanding.” Notice he distinguishes his own spirit from his understanding, his rational, sentence-making mind. There is a kind of prayer in which the believer's spirit is praying while the understanding is not forming or interpreting the words. For some believers that includes the gift of tongues, which Scripture treats as genuine, never as proof of a higher spiritual rank.
When you can't find the words
And there is a deeper comfort still. “The Spirit also helps in our weaknesses. For we do not know what we should pray for as we ought, but the Spirit Himself makes intercession for us with groanings which cannot be uttered.” This is not the same thing as tongues; it is the Holy Spirit's own intercession on your behalf when you are too broken or exhausted to pray at all. In those seasons you are not disconnected from God. The Spirit is carrying to the Father what you cannot put into words.
So praying in the Spirit is not a graduation you have to reach. It is grace for the limits of your own strength and language. Whether it comes as an ordinary prayer offered from your union with Christ, a prayer language, or a wordless weariness the Spirit lifts on your behalf, the point is the same: your prayers were never confined to what your mind could compose. When you run out, He does not, and He carries you the rest of the way to the Father.