Romans 8:26-27 meaning

Paul mentions in verse 4 that when believers walk in the Spirit, they fulfill the law. This is a reiteration of the contrasting point Paul makes against the competing Jewish "authorities" who slandered his teaching to the believers in Rome (Romans 3:8). It seems probable that this letter is also a defense for Paul's friends Aquila and Priscilla (who host a church in Rome) to use against the competing Jewish "authorities" (Romans 16:3-5; Acts 18:2, 18, 26). 

The slanderers claim they are champions, saving the law from the heretical teaching of Paul. Paul says the law is no longer our authority, the Spirit is our authority.

The Holy Spirit is given to believers as a Helper (John 14:16, 17, 26), in the same way the Spirit also helps our weakness (v 26). One of the ways that the Holy Spirit helps us is in our communication with God. Because we still have a sin nature and are weak, we often don't know how to talk with God, for we do not know how to pray as we should (v 26). So, the Holy Spirit Himself intercedes for us with groanings too deep for words (v 26). He serves as our voice, our helper, to communicate to God for us.

One simple example of this is how a babysitter might need the help of one of the older children they are babysitting, to help them understand what the younger sibling (perhaps a toddler) is asking for. We are weak and flawed, the Holy Spirit helps us (in our weakness) and intercedes for us. Jesus also interceded for us to God in His sacrifice on the cross (v 34). In a similar way, the Holy Spirit is given to believers to intercede for them to God.

So, even in the suffering and the tribulations we experience on this earth, we have the Holy Spirit to help us in our weakness. In contrast to the competing Jewish "authorities" who claim we can adhere to the law and become righteous, Paul insists we can only achieve righteousness through dependence upon Christ and His Spirit, both to gain the new birth and forgiveness of sins as well as to walk in the newness of life with the resurrection power.

Paul refers to the Holy Spirit as He who searches the hearts (v 27). This is one of the ways that the Holy Spirit helps our weakness so that He can intercede, or speak on our behalf, to God. He knows what the mind of the Spirit is, because He intercedes for the saints according to the will of God (v 27). 

This should be a great encouragement to all of us, that the Spirit prays for us according to the will of God, even when we don't know how to. Paul has already told his audience that one of the primary things that the Holy Spirit does is give believers life in their mortal bodies, providing the ability to do God's will (verses 5-16) This ministry to intercede to God on our behalf is another way the Spirit helps us in our weakness.