The score dialog is the control-center for anything at score-level rather than note-level. This is the place to go to whenever you'd like to change the order of voices, alter instrumentation, combine two voices on one staff, prepare part-extractions and so on. Click on any button in the picture above to get more information.
The first column displays the part number. The main part is the underscored one. The main part is responsible for Bar lines in all voices, so meter and hard bar line placement are to be corrected in the main voice.
The part with an arrow signals the current part. By clicking on the first column you can select the current part. The part-tab will show detailed information about the current part.
Dragging a row using the first column will alter the order in which the parts are displayed within a score see also
Right clicking will popup a context menu in which you can enable whether a part is visible, audible and main part.
The Score checkmark at the bottom left of the dialog enables single part view for easy part extraction. As long as score-view is enabled multi-rests will be expanded.