When the frequency of sound waves match the resonant frequency of a structure, like a building or a window, resonance occurs which is clearly visible. This frequency depends upon the material and it's dimensions. So will a molecule, with a given structure, have such a characteristic frequency? I'm not really clear with the concept, a detailed explanation would be helpful.
Yes it will, here is a simple example:
Imagine a long molecule with a central atom in it to which two chains of other atoms are attached. Since the bonds consist of shared electrons and the physical positions of those electrons cannot be pinned down at any instant, it is natural to expect that there might be a little springiness or "give" in those bonds. This means that if you hit the molecule with the right frequency of excitation, the molecule will resonate and wiggle back and forth with the masses of the different parts of the molecule furnishing inertance and the springiness of the bonds furnishing the compliance.
For a complicated molecule, there will be a number of resonances that can be excited, corresponding to bending modes, longitudinal modes, even twisting or rotational modes. The frequencies of those modes carry information about the details of the molecule's structure and so it is possible to explore that structure by shining light of different frequencies at a large collection of those molecules and looking for the resonances (where the molecule strongly absorbs that frequency of light).
For organic molecules, many of the most important resonances are in the infrared part of the electromagnetic spectrum, and thus you have the field of IR spectroscopy.
Resonance occurs when a system (of any size) which can oscillate, is driven by an oscillating external force at a frequency which matches the non-driven frequency of the system. A standing wave can be considered a resonant condition which results when the reflections from boundaries maintain a fixed phase difference.