Widget: a widget is an element of an graphical interface such as a container window, a button or a field for entering text.
Layout management: this term describes the way in which widgets are arranged in a window. In its simplest form, an element may be placed at a specific position and given a specific height and width. But when the user resizes the window, the widgets should stay in their position and change their size accordingly. Linux allows to do that by using layouts to place the widgets in.
Signal and slot: Signals and slots are used for communication between objects. The signal/slot mechanism is a central feature of Qt. Signals are emitted by objects when they change their state in a way that may be interesting to the outside world. Slots can be used for receiving signals, but they are normal member functions. You can connect as many signals as you want to a single slot, and a signal can be connected to as many slots as you desire. Please see the TrollTech documentation on signals and slots for more details. In the (excellent) online documentation that comes with Qt you'll find the signals and the public slots that go with each class. You can then implement your own slots.