How to get a (descriptive) overview of a large database?
There's no way to have a complete summary of a large dataset like this, you have to analyze what can be relevant, decompose into more specific pieces of information and then find the best way to visualize each specific part on its own.
The first thing would be to plot the distribution of this parameter of interest across subjects and/or observations.
If you want to look at the individual level and there are too many values, you can simply pick a random subset (say 100 subjects) and plot these. Then you do it again with a different random subset in order to distinguish real patterns from variations due to chance.