Final answer:
The pairing of chromosomes essential for crossing over is known as synapsis, which occurs during prophase I of meiosis and is mediated by the synaptonemal complex.
Step-by-step explanation:
The pairing of chromosomes along their lengths, which is essential for crossing over, is referred to as synapsis. During prophase I of meiosis, the homologous chromosomes are brought into close alignment with each other. This tight pairing, facilitated by a synaptonemal complex, is necessary for the precise alignment of genes on the chromatids of the homologous chromosomes, which allows for the process of crossing over to occur. Crossing over, the exchange of chromosomal segments between homologous non-sister chromatids, introduces genetic diversity and can be observed as chiasmata under a microscope.