To check it or uncheck it; that's the question. It's the "Contiguous" option you see in Photoshop when you use the "Magic Wand," the "Magic Eraser," the "Background Eraser," the "Paint Bucket" and other tools. Basically, "contiguous" means touching or connected. In Photoshop, it describes pixels of the same colour touching each other.
When you drag the "Magic Wand" to an area of colour in a Photoshop image and click, it magically selects a shape with contiguous pixels of the same colour. However, if you uncheck "Contiguous," the "Magic Wand" will select every pixel of that colour, whether touching or not. You can also raise the "Tolerance" setting to select a broader range of contiguous colours.
Click the area you want to erase in your image, and select "Contiguous" to erase only those pixels actually touching the pixels you clicked. Deselect, or uncheck, "Contiguous" to erase all similar pixels in the image. If you also check "Anti-aliased," it will smooth the edges of your selection. Keep "Opacity" slider at 100 per cent to erase pixels completely; lower it if you just want to partially erase pixels.
Before you dump that "Paint Bucket" into your image, take a look at the "Contiguous" setting. If you want to paint only those same-coloured pixels contiguous to the ones you click, leave "Contiguous" checked. If you want to paint all the pixels that are the same colour as the one you checked, uncheck the "Contiguous" setting. Then, the "Paint Bucket" will fill them all with the foreground colour shown in the small boxes on the toolbar at your left.
Be sure you are on the layer with the background you want to erase. Then, in the top toolbar, select "Limits" for erasing. "Contiguous" will erase only the pixels of the sampled colour that are connected to each other. "Discontiguous" will erase the sampled colour wherever it occurs when you drag the eraser across the background.