Homologous chromosomes are chromosomes that contain the same genes, but may have different alleles for those genes.
In a homologous pair, one chromosome comes from the mother and the other from the father.
Sister chromatids contain the same genes (ie: they code for the same proteins), whereas non sister chromatids do not.
Above is a single chromosome. As you can see, this chromosome has 2 strands. Each of these strands is called a chromatid. Because these chromatids have the exact same genes and alleles, they are called sister chromatids.
Above are 2 chromosomes. One comes from the mother, the other from the father.
If these 2 chromosomes have the exact same genes, then they are said to be homologous.
However, even though they may have the same genes, there may be slight variations in the base sequences, meaning that they have different versions of the same genes.
For example, both chromosomes have a gene that codes for eye colour, but the one from the mother codes for brown eye colour, and the one from the father codes for green eye colour.