Non-sister chromatids are chromatids of homologous chromosomes.
During cell division each chromosome needs to replicate, this ensures that the each daughter cell gets a complete set of chromosomes, which produces sister chromatids. These chromatids contain the exact same genes and the exact same alleles - the chromatids are exact copies of each other.
Every chromosome has a homologous pair, one from the mother (maternal) and one from the father (paternal), these homologous pairs contain the same genes but may contain different alleles, there are not exact copies of each other and are called non-sister chromatids.