Phil 3:10 that I may know Him and the power of His resurrection, and the fellowship of His sufferings, being conformed to His death,
11 if, by any means, I may attain to the resurrection from the dead.
12 Not that I have already attained, or am already perfected; but I press on, that I may lay hold of that for which Christ Jesus has also laid hold of me

That's progressive sanctification. The goal is to become completely like Jesus, to parttake fully in his divine nature (2 Peter 1:4) and thereby attain to the resurrection from the dead. The last component is obtaining a new, glorified body and that will not happen until in afterlife but the rest one may press on towards during this lifetime.

What does it mean to be conformed to his death ?

Romans 6:10 For the death that He died, He died to sin once for all; but the life that He lives, He lives to God.
11 Likewise you also, reckon yourselves to be dead indeed to sin, but alive to God in Christ Jesus our Lord.

It starts with renewing one's mind according to verse 11 and the goal is to become as dead to sin as Jesus became through his death. Not just as an attitude in the mind but in the heart, through and through.

What about the fellowship of his sufferings ? Should one endure the physical and emotional pain of the torture, the crucifixion, the shunning, the treason, the mockery and the moment of death that Jesus suffered at the hands of men ? The onslaught of demonic oppression described in Psalm 22 ? The wrath of God described in Psalm 18 ? The soul being poured out unto death etc described in Psalm 18 ? Facing eternity in hell as described in Jonah 2 ?

Nope, Jesus carried that for us so that we would not have to bear it. But we may parttake in his conclusion from enduring and overcoming that.

Gal 6:14 But God forbid that I should boast except in the cross of our Lord Jesus Christ, by whom the world has been crucified to me, and I to the world.

Heb 13:12 Therefore Jesus also, that He might sanctify the people with His own blood, suffered outside the gate.
13 Therefore let us go forth to Him, outside the camp, bearing His reproach

Romans 6:1 What shall we say then? Shall we continue in sin that grace may abound? 2 Certainly not! How shall we who died to sin live any longer in it? 3 Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? 4 Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life.
5 For if we have been united together in the likeness of His death, certainly we also shall be in the likeness of His resurrection, 6 knowing this, that our old man was crucified with Him, that the body of sin might be done away with, that we should no longer be slaves of sin. 7 For he who has died has been freed from sin. 8 Now if we died with Christ, we believe that we shall also live with Him, 9 knowing that Christ, having been raised from the dead, dies no more. Death no longer has dominion over Him. 10 For the death that He died, He died to sin once for all; but the life that He lives, He lives to God. 11 Likewise you also, reckon yourselves to be dead indeed to sin, but alive to God in Christ Jesus our Lord.
12 Therefore do not let sin reign in your mortal body, that you should obey it in its lusts. 13 And do not present your members as instruments of unrighteousness to sin, but present yourselves to God as being alive from the dead, and your members as instruments of righteousness to God. 14 For sin shall not have dominion over you, for you are not under law but under grace.