What are some insights from looking at Bode plots
The bode plot is a representation of the bigger picture. That bigger picture is the pole zero diagram: -



The top three images (all bode plots) give you different examples of a 2nd order low pass filter. The bottom left picture shows you the bigger picture - it combines the bode plot with the pole zero diagram i.e it's 3D. Bottom right is the view of the 3D image looking down from above - this is the pole zero diagram I mentioned and this contains all the mathematical information for a system or filter.

The bode plot is a simplification of the pole zero diagram but, importantly it shows you directly the response of a filter (or system) in terms of amplitude and frequency (jw).

If some of these concepts are too difficult right now then that's understandable.