The part after : is called “initializer list. It is a ,-separated list of expressions that can access constructor parameters and can assign to instance fields, even final instance fields. This is handy to initialize final fields with calculated values.
The initializer list is also used to call other constructors like : ..., super('foo').
Since about Dart version 1.24 the initializer list also supports assert(...) which is handy to check parameter values.
The initializer list can’t read from this because the super constructors need to be completed before access to this is valid, but it can assign to this.xxx.
Pointing out as mentioned in the comments by user693336:
This also means the initializer list is executed before the constructor body. Also the initializer lists of all superclasses are executed before any of the constructor bodies are executed.
Example (copied from https://github.com/dart-lang/language/issues/1394):
class C {
final int x;
final int y;
C(this.x) : y = x + 1;
}