Почему не срабатывает def on_change(не вставляется картинка)?

Попробуйте так:

import sys
from PyQt5.Qt import *

class Background(QDialog):
    background_bottom = ''
    background_top = ''

    def __init__(self):
        super().__init__()

        self.width = 400
        self.height = 400
        self.title = 'Background'

        self.init_window()
        self.center()
        self.init_ui()

        self.combobox.activated.emit(0)                                 # +++
#        self.show()

    def init_window(self):
        self.setGeometry(0, 0, self.width, self.height)
        self.setWindowTitle(self.title)

    def center(self):
        qtRectangle = self.frameGeometry()
        centerPoint = QDesktopWidget().availableGeometry().center()
        qtRectangle.moveCenter(centerPoint)
        self.move(qtRectangle.topLeft())

    def init_ui(self):
        root_layout = QVBoxLayout()
        self.combobox = QComboBox()

        self.combobox.activated.connect(self.on_change)                  # +++

        self.combobox.addItem('Contrast')
        self.combobox.addItem('Monako')
        root_layout.addWidget(self.combobox)
        self.background_layout = QHBoxLayout()                         
        root_layout.addLayout(self.background_layout)
        buttons_layout = QHBoxLayout()
        buttons_layout.setAlignment(Qt.AlignRight)
        button_ok = QPushButton('Ok')
        button_ok.clicked.connect(self.post_background)
        button_cancel = QPushButton('Cancel')
##        
# ?       button_cancel.clicked.connect(self.cancel)
        buttons_layout.addWidget(button_ok)
        buttons_layout.addWidget(button_cancel)
        root_layout.addLayout(buttons_layout)
        self.setLayout(root_layout)

#        self.combobox.currentIndexChanged.connect(self.on_change)        # ---


    def on_change(self, index):
        if index == 0:
            # Не работает
            label = QLabel()
            pixmap = QPixmap('Ok.png')                                    #('./temp/contrast.png')
            label.setPixmap(pixmap)
            self.background_layout.addWidget(label)
            label.show()

    def post_background(self):
        background = self.combobox.currentText()
        if background == 'Contrast':
            self.background_top = 'white'
            self.color_top = self.background_bottom
            self.color_bottom = self.background_top
            self.background_bottom = 'black'
        elif background == 'Monako':
            self.background_top = 'black'
            self.color_top = 'white'
            self.background_bottom = 'yellow'
            self.color_bottom = 'black'
        self.close()
        return self.background_top, self.background_bottom, self.color_top, self.color_bottom


if __name__ == "__main__":
    app = QApplication(sys.argv)
    w = Background()
    w.show()
    sys.exit(app.exec_())