Each red, blue, yellow, or green butterfly-shaped structure in the animation represents one chromosome that has replicated so that it's sister chromatids remain joined at their centromeres. When the chromosomes move together and pair up, they are called a homologous pair. The four chromatids together are called a tetrad and the process of pairing up is referred to as synapsis.
While paired, non-sister chromatids from opposite chromosomes touch and perform crossing over.
Then the chromosomes are pulled to opposite poles of the cell by the spindle fibres. However, which member of each chromosome pair gets pulled to which pole is random. This is called "independent assortment". In this animation, two different possibilites are illustrated so that the daughter cells produced are different in both cases. In reality there are many different possibilities and this leads to genetic variation in the daughter cells (gametes) and hence in the offspring.