A part is a project, activity, routine, or task that takes up (or will take up) a portion of the 24 hours that you have in every day. Every minute of each day is "occupied" by one part or another. Parts are distinguished for the purpose of creating Now-Next integrity. Some parts of your day may already enjoy Now-Next integrity.
For example, one part of your day is reading a bedtime story to your two children. Typically both your Now and your Next are both quite happy about doing that, both to plan it and to enjoy doing it. In contrast, your Next wants to spend at least 20 minutes each day for a while to get caught up on some bookwork for taxes. But for this part (spending 20 minutes a day on bookwork) your Now is dragging his or her feet and keeps distracting you with other things. This is a part of your day that you currently have not found a way to have Now-Next integrity with.
This distinction of parts is helpful in creating and understanding the distinctions of prioritizing process over results and its two components of process prioritization #1 (PP1) and process prioritization #2 (PP2). See What's the full idea of process first? and the Doer and the Planner.