The author's excellent 'powers of observation' [=ability to notice and pay close attention to things] are evident in the book's detailed descriptions.
The plants seem to have recovered from the disease, but they are still 'under observation'. [=someone is watching them carefully]
They're keeping him at the hospital 'for observation' [=so that doctors can watch him carefully] for another few days.
(..) Frodo! Someone at the door. In fact,it has been remarked by some... ... that Hobbits' only real passion is for food. A rather unfair observation... ...as we have also developed a keen interest in the brewing of ales... ...and the smoking of pipe-weed. But where our hearts truly lie... (..)2001 The Lord of the Rings: The Fellowship of the Ring