What is the function of the nucleus in the sperm cell?
The sperm nucleus (in animals) contains the haploid chromosome set of the parent father. The egg or ovum carries the other half of the chromosome set from the parent mother. On fertilisation the two sets fuse and a full set of chromosomes forms (diploid). The cell then divides through mitosis to form the embryo.
The nucleus also helps control the sperm cell while it seeks out the ovum.
In plants a similar structure develops when a pollen grain (male) germinates on the stigma of a receptive flower. A pollen tube grows down the style to deliver the nucleus to the ovary of the flower [simplified explanation!].