In theory, the answer is: A partial view is a “sub-view” that you embed within a main view – something that you might reuse across multiple views, like a sidebar.
In practice, the answer is: Very little.
In theory, partial views are more lightweight than standard views, but it’s perfectly OK to pass a “regular” view to RenderPartial and the performance seems to be exactly the same. I frequently use regular .aspx views as “partial” views because you can make them reference a master view in order to provide templated content like what you can do with UserControls in ASP.NET WebForms. See here.
Partial views are more like web parts on a portal – they are completely self-contained objects. Use them if the layout is simple and static, or if you’re annoyed by the Intellisense errors when you don’t have the <html> and <body> tags in a standard View.