Philadelphia style ice cream is what most of us would refer to simply as 'ice cream'.
At some point in the mid 1800s, ice cream vendors in Philadelphia started making ice cream without any eggs in. This was new, as the traditional 'French style' ice cream used egg yolks to make a rich custard base. The new eggless recipe resulted in a lighter, fluffier ice cream, and, as it happens, also eliminated the time-consuming step of cooking the custard base (the milk and sugar base is still heated, however, to allow for a smoother mix).
This advancement was not simply a matter of Americans being too cheap and lazy to add in the custard; custard is a stabilizer, keeping the water in the ice cream from forming large crunchy ice crystals. Another way to reduce crystals is to frequently stop churning and scrape the sides of the churn, breaking up the ice crystals as they form. In 1843, Philadelphian inventor Nancy Johnson patented an "artificial freezer" which included, among other advancements, internal dashers that scraped the sides while churning. Another technological advancement, the construction of warehouse-sized ice houses to provide ice year-round, also supported the local ice cream boom.
Americans also tend to eat ice cream in the 'American hard-pack style', which is frozen hard, as opposed to soft-serve. However, soft-serve does not necessarily mean the pseudo-cream goop that is popular at Dairy Queen, but also fancier ice creams such as gelato.
As Philadelphia style ice cream spread, it was sometimes alternatively referred to as American or New York style ice cream, and these labels are still in use.