2 Timothy 2:8b

Paul says to remember Jesus Christ. He then mentions that Jesus was raised from the dead and is a descendant of David. Being a descendant of David, he is in fulfillment of some of the Old Testament prophecies. The Messiah was prophesied to be an offspring of David. Not only are we to remember that he defeated death, but that his coming was prophesied and he fulfilled these prophecies. This was all part of a plan for which he was the best and first choice for the part. He's the only choice for the part, since no one else could fill his shoes (or sandals).

This Jesus who saves is the one who Paul preached and still preaches in his gospel. Not that Paul owns or originates the gospel, but he is referring to the one he preaches as opposed to people who preach a different and false gospel. There were people distorting the gospel, so perhaps it was important to clarify this point. This part of the gospel preached by Paul, and it is important to remember Jesus and the gospel.