"We have come to share in Christ if we hold firmly till the end the confidence we had at first. As has just been said: 'Today, if you hear his voice, do not harden your hearts as you did in the rebellion.'" NIV translation
Paul repeats the quote from Psalms as it speaks to the issue of trusting God. Once again, there are people who misinterpret Paul's use of the phrase "hold firmly" to say that he is warning of losing our salvation but that is not what he is saying. He says that we are to hold onto the confidence that we had at first but what confidence is he talking about? He is speaking of the confidence that we are saved by grace through faith in Jesus Christ. If we hold fast to that (and we will if we are in Christ) then nothing can separate us from Him. If we come to Christ trusting in Him for our righteousness, then we do not have to worry about stumbling and losing what we have been given. All the Jews had to do was to believe that God had given them the promised land and to take hold of it. It is the same with Jesus and our salvation; just grab it!
"Who were they who heard and rebelled? Were they not all those Moses led out of Egypt? And with whom was he angry for forty years? Was it not with those who sinned, whose bodies fell in the desert? And to whom did God swear that they would never enter his rest if not to those who disobeyed? So we see that they were not able to enter, because of their unbelief." NIV translation
The rest that is spoken of, here, is different than the rest of salvation.
This rest speaks of God's provision in the world for today. As with Israel when they refused to enter the promised land, we, as Christians, can choose to doubt God's provision for all of our needs. If we do so, we (like Israel) will get a wilderness experience where we learn that God is the provider and sustainer. We can chase around looking for the blessing or we can accept what Jesus has done and is willing to do. If we are His, then, He will allow us to rest in Him and know that He is our Sustainer. If we believe and trust in Him, then, we will be blessed (not have to worry) about our food, clothes, shelter, etc.