Benefactory, the subject in 1 Cor 15 is whether Christ truly rose from the dead. And the argument is that if Jesus did not rise from the dead, then the gospel is false and we are believeing a gospel which cannot save. The definition of vain here means empty, or devoid of truth.
1 Cor 15:12 Now if Christ be preached that he rose from the dead, how say some among you that there is no resurrection of the dead?
13 But if there be no resurrection of the dead, then is Christ not risen:
14 And if Christ be not risen, then is our preaching vain, and your faith is also vain.
15 Yea, and we are found false witnesses of God; because we have testified of God that he raised up Christ: whom he raised not up, if so be that the dead rise not.
16 For if the dead rise not, then is not Christ raised:
17 And if Christ be not raised, your faith is vain; ye are yet in your sins.
18 Then they also which are fallen asleep in Christ are perished.
19 If in this life only we have hope in Christ, we are of all men most miserable.
And you see verse 19 it says "If in this life only". If there is no resurrection from the dead, then the best thing a man can do is eat, drink, and be merry. Christians give up many of the worldly pleasures for Christ, if Jesus did not rise up from the dead, then neither will we, and all our sacrifices for Christ are vain and useless. This is what this chapter is talking about.