Odours are just molecules that are detected by the cells in our noses, and it's possible to identify them with various techniques. You've probably heard of mass spectrometry, which tells you the mass to charge ratio of the molecules that are present in a sample. You can figure out which molecules they are by looking up the m/z value in a database -- but mass spectrometers are pretty bulky.

There's also a technique called field-asymmetric ion mobility spectrometry, which gives you a less direct indication of the molecules you're looking at, but FAIMS can be miniaturized into a silicon chip, and that is what Owlstone has done. Here's a bit more info about FAIMS: https://www.owlstonemedical.com/science-technology/faims-tec...

edit: odours are not necessarily organic molecules