Refers to the fine points or specific parts of something, often used when examining or explaining something thoroughly.
Let's discuss the details of the plan.
He pays attention to the smallest details.
He's a person who is particular about the details of his work.
I explained the plan down to every detail.
I checked the details of the contract before signing.
The designer finished the piece paying attention to every last detail.
全体 refers to the whole of something, in direct contrast to 細部, which refers to its small individual parts.
Compound of 細 (さい, 'fine, minute') and 部 (ぶ, 'part, section').