[NSDate date] is a factory method for constructing an NSDate object.
If you read the guide “Using Swift with Cocoa and Objective-C”, there is a section on interacting with Objective-C apis:
For consistency and simplicity, Objective-C factory methods get mapped as convenience initializers in Swift. This mapping allows them to be used with the same concise, clear syntax as initializers.”
Excerpt From: Apple Inc. “Using Swift with Cocoa and Objective-C.” iBooks. https://itun.es/gb/1u3-0.l
So the factory method:
[NSDate date]
is converted into an initializer in Swift
NSDate()
It’s not just NSDate where you will find this pattern, but in other Cocoa API’s with factory methods.