I believe you are referring to 'stretching' the tires, or putting a tire that is slightly narrower than the wheel, on said wheel. This would be 98% aesthetics; there may be a small number of occasions where a minimal stretch will be used to increase sidewall stiffness, thus improving responsiveness and reducing deflection, but this is not always the case.
In general, the main thing to look out for is to whether the tire size chosen for any given wheel conforms to the tire manufacturer's recommended wheel widths. Any given tire size will have a range of acceptable wheel widths it will fit; this information is readily available on any tire manufacturer's website or often tire retailer websites such as
www.tirerack.com.
Stay within manufacturer recommended specs and you will be good. That said, doesn't hurt to go with a wider tire option when available!