Paul not only chose to forsake all of his earthly advantages to follow Christ, but he also greatly desired to know Jesus in three specific ways. First, he wanted to know "the power of His resurrection". Christianity is founded upon Jesus' resurrection from the dead (cf. I Cor. 15), which clearly indicates the power and significance of it. Paul wanted to understand to the fullest all of the implications of that resurrection (e.g., the hope of eternal life, the comfort in death, the motivation to live a godly life, etc.).
Second, Paul wanted to know "the fellowship of His sufferings". Jesus, even before He was hung on the cross, suffered greatly at the hands of blasphemous enemies. Unlike some saints who do not even want to be inconvenienced for the sake of worshipping or serving Christ, Paul wanted to suffer for Jesus--and in the same ways that Jesus suffered! Paul certainly knew the Lord quite well in this area. The apostle endured much suffering for the name of Christ, as II Corinthians 11:22ff highlights. He was beaten severely many times, stoned, shipwrecked, in great danger often, etc. In fact, as he penned this epistle he was in prison.
Third, Paul wanted to be "conformed to His death". Paul was willing to die for the Lord, even by crucifixion, if he was called to do so. He wanted to know Christ fully in his life and in his death. His aim was to pattern his existence fully after Jesus in every way. He would magnify Christ "whether by life or by death" (Phil. 1:20).
These are tremendous thoughts from the apostle Paul--are they not? He gave up everything for Christ and exhorts us to do the same that we may be found among the faithful on the final day. What greater ambition can a person have than this? May we, like Paul, have a desire for heaven and a willingness to sacrifice everything to make it a reality!