What happens to the phenotype of the heterozygotes when traits are inherited in an incomplete dominance pattern?

"Dominant" is a highly generalized term that we use to describe the relationship of a particular allele to another. Dominant alleles will be more visible in the phenotype of the organism. In reality, things aren't always so straightforward, as the idea of being "visible in the phenotype" depends on much more than the allele itself. Thus, it should come as no surprise that there are variations on dominance.
Incomplete dominance describes a situation where two alleles are equally expressed, but segregated. That is to say, some cells express one allele exclusively, and other cells express the other allele exclusively. Flowers are commonly cited as an example of incomplete dominance, wherein different parts of the flower can have different colors and patterns with no apparent relationship to the physical structure of the flower. There aren't many obvious traits in humans that involve incomplete dominance; if, for example, an allele for black hair and an allele for blonde hair were codominant, we would expect to see heterozygotes that have "patchwork" hair with intermittent chunks of black or blonde depending on where they're located.
Incomplete dominance is often compared and contrasted with codominance, another variation in which both alleles are equally expressed but not equally visible at the phenotypic level; instead, their equal expression "blends" to create a new phenotype. This is usually because the rates of expression per unit area are the same for a codominant trait, whereas the segregated effect of incomplete dominance leads to visibly different regions of the organism which retain a single allele's characteristics.