Longer, lower, wider and, therefore larger and heavier, was the general trend for American automobiles during the 1950s and 60s. Yes, "compact" cars were introduced around 1960, but these too tended to grow over time. (This isn't a strictly American thing. Consider the Honda Civic, a very small car in its first version and now just a notch smaller than its "standard size" sibling, the Honda Accord.)
The present post deals with the "wider" aspect of that growth. Some designs simply had fenders bulge out. But for a while there was a fashion of having "catwalks" on either side of the passenger compartment -- flat extensions between the side windows and the drop-off zone of the fender/side of the car. This will be made clear in the illustrations below.
I recall reading someplace back in that era that such catwalks, if they had an outer ridge, would serve to nest or cradle the passenger compartment "tumblehome" (that's a styling term for the part of the passenger compartment with the roof and windows).
The visual result was often pleasant. Moreover, the wide sides in theory could have contained substantial steel beams for side-collision protection. But fuel crises starting in 1973 and later fuel mileage regulations forced automobile designers to reduce the size and weight of vehicles. An easy way to reduce weight is to narrow a car, and that practice pretty well ended the fashion of wide catwalks.
Here are examples of broad-shouldered cars from that era.
The Tempest and Skylark shared the same basic body, so styling details were superficial elements General Motors used to visually distinguish brands.
This Thunderbird's shoulders are more rounded than catwalk-like, but the ridge near the top of the fender stiffens the appearance of that section of the car.
Here is a particularly strong example. We see both a catwalk and ridge setting off the tumblehome.
The same might be said of this Chrysler, though the catwalks seem a bit narrower than the Mercury's.
This Continental appeared towards the end of the catwalk era; again they are narrow.