The phrase ‘manifestation of the Spirit’ appears only once in the Bible, in 1Cor. 12:7:
To each is given the manifestation of the Spirit for the common good.
Here it is used to describe the various gifts of the spirit: the spirit gifts were ‘manifestations of the spirit’.
‘Manifestation’ means something like ‘the act of demonstrating’,1 or an ‘an open display’ of something,2 so the spirit gifts were ‘demonstrations’ of the holy spirit.
1. Collins English Dictionary (HarperCollins Publishers, 2003)
2. Cf. the same Greek word as used in 2Cor. 4:2 (HCSB).