The Center Recording on Cursor option enables the selection rectangle to follow the cursor when recording from screen. It can be useful if you want to record only a part of the screen, but occasionally need to capture something that is happening outside the original selection. This option is only available when a custom selection area has been selected using the Selection Tool, but not when either the entire desktop or a specific window have been selected for recording.
The Zoom options allow you to focus in or away from the selected recording area. To change the zoom during recording, select a new zoom percentage from the Screen Capture -> Zoom submenu, or use the corresponding system-wide hot-keys, which can be configured in Options -> Hot-Keys. The default zoom level is Fit to Output, which scales the contents of the selected area to match the dimensions of the output recording. Using custom zoom levels allows control over how much scaling is applied, but if the output dimensions don't match the selection dimension, then the contents of the selected area may be cropped or the recording may show areas outside the selected area: