What is the Giemsa staining of chromosomes?
Giemsa is not a particular methid to stain malaria or any other parasite. It stains DNA. As such, it can be used to stain any DNA-containing organism, or, in other words, any known cell.
Regarding its particular use in chromosomal banding, you can refer to many online resources, such as this one of the University of Washington:

Chromosomes in metaphase can be identified using certain staining techniques, so called banding
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G-bands are most commonly used. They take their name from the Giemsa dye, but can be produced with other dyes. In G-bands, the dark regions tend to be heterochromatic, late-replicating and AT rich. The bright regions tend to be euchromatic, early-replicating and GC rich.