What do curly braces wrapping constructor arguments represent?

This makes the argument a named optional argument.

When you instantiate a Person you can

Person p;
p = new Person(); // default is _newDbConnection
p = new Person(connectionFactory: aConnectionFactoryInstance);

• without {} the argument would be mandatory
• with [] the argument would be an optional positional argument

// Constructor with positional optional argument
Person([this.connectionFactory = _newDBconnection]);
...
Person p;
p = new Person(); // same as above
p = new Person(aConnectionFactoryInstance); // you don't specify the parameter name

Named optional parameters are very convenient for boolean arguments (but of course for other cases too).

p = new Person(isAlive: true, isAdult: false, hasCar: false); 

There is a specific order in which these argument types can be used:

1. mandatory (positional) arguments (only positional arguments can be mandatory)
2. optional positional arguments
3. (optional) named arguments (named arguments are always optional)

Note that positional and named optional arguments use a different delimiter for the default value.
The named requires : but the positional requires =. The language designers argue that the colon fits better with the Map literal syntax (I would at least have used the same delimiter for both).

= is supported as delimiter since Dart 2 and preferred according to the style guide while : is still supporzed.

See also:

• What is the difference between named and optional parameters in Dart?
• Functions Are Fun, Pt 1 – Dart Tips, Ep 6
• Chapter 2. A Tour of the Dart Language – Functions
• Chapter 2. A Tour of the Dart Language – Constructors