まずは普通に


class Model {
  var value: Int
  init(value: Int) {
    self.value = value
  }
}

let model = Model(value: 0)
print("\(model.value)")

結果は
0

ではプロパティを明示的にNotNullと宣言する


class Model2 {
  var value: Int!
  init(value: Int) {
    self.value = value
  }
}


let model = Model2(value: 0)
print("\(model.value)")

結果は

Optional(0)

追記

Apple Swift version 3.0 (swiftlang-800.0.46.2 clang-800.0.38)
Target: x86_64-apple-macosx10.9
/Applications/Xcode8.app/Contents/Developer/usr/bin/lldb "--repl=-target x86_64-apple-macosx10.9 -enable-objc-interop -sdk /Applications/Xcode8.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.12.sdk -color-diagnostics"
Welcome to Apple Swift version 3.0 (swiftlang-800.0.46.2 clang-800.0.38). Type :help for assistance.
  1> class Model2 {
  2.   var value: Int!
  3.   init(value: Int) {
  4.     self.value = value
  5.   }
  6. }
  7.
  8.
  9. let model = Model2(value: 0)
 10. print("\(model.value)")
Optional(0)

Apple Swift version 2.2 (swiftlang-703.0.18.1 clang-703.0.29)
Target: x86_64-apple-macosx10.9
/Applications/Xcode.app/Contents/Developer/usr/bin/lldb "--repl=-target x86_64-apple-macosx10.9 -enable-objc-interop -sdk /Applications/Xcode8.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.12.sdk -color-diagnostics"
Welcome to Apple Swift version 2.2 (swiftlang-703.0.18.1 clang-703.0.29). Type :help for assistance.
  1> class Model2 {
  2.   var value: Int!
  3.   init(value: Int) {
  4.     self.value = value
  5.   }
  6. }
  7.
  8.
  9. let model = Model2(value: 0)
 10. print("\(model.value)")
0

Swift3からみたい