What kinds of information does a structural formula reveal about the compound it represents?
This question is very vague, as the structural formula can show a multitude of properties relative to other similar structural formulas or as part of a trend.
For example, the boiling point can be shown dependant on the bonding, which could lead to dipoles or hydrogen bonds being formed. Also, the length/ size of the molecule can affect its density, boiling point, solubility, etc.
It can also help in naming the molecule, as many compounds with the same molecular formula have different structural formulas, for example cycloalkanes and alkenes, or aldehydes and ketones.