Final answer:
Prophase I is the meiosis stage where DNA condenses into visible chromosomes, the nuclear envelope starts to disintegrate, and homologous chromosomes pair up.
Step-by-step explanation:
The stage of meiosis characterized by DNA condensation into compact chromosomes is Prophase I. During Prophase I, the nuclear envelope begins to break down, and the chromosomes condense. Centrioles start moving to opposite poles of the cell, and a spindle begins to form. This phase is distinct because homologous chromosomes pair up, a step not seen in Prophase of mitosis or Prophase II of meiosis. Crossing-over, which is crucial for genetic diversity, also occurs during this phase.