The phrase "finer details" refers to specific and small elements of something that may not be immediately noticeable, but are important and add to the overall quality or understanding of that thing. Full definition
Last but not least, pictures and tables are treated equally in terms of a zoom - in function enabling readers to look closer in finer details of images. (bbebooksthailand.com)
The video is the first time scientists have been able to see in fine detail how carbon dioxide moves through the atmosphere, showing the source of greenhouse emissions and their destination. (pearltrees.com)
There's not a great amount of fine detail on display, but that could be a product of the lenses used or the film stock of the period. (filmfreakcentral.net)