Unlike a regular Mac computer or Windows PC, the screen resolution of the iPad is "fixed", and cannot (currently) be changed. Since the iPad lets you rotate it to change between landscape mode (horizontal) and portrait orientation (vertical), its screen resolution actually varies. In portrait orientation, the iPad's screen resolution is 768 pixels wide by 1024 pixels high; in landscape mode, your iPad displays 1024 pixels horizontally, and 768 pixels vertically - in other words, the distribution of the screen resolution's sides changes, but not the total screen resolution itself.
Ideal iPad background image size
In most cases, you will not care much about screen resolution, since applications are optimized for the device, and most iPhone apps are being re-designed to make the best of the larger iPad display size. Websites viewed in Safari (or other web browsers for the iPad) can be zoomed in or zoomed out as needed, to see more content or more details on a given web page.
The common importance of screen resolution is when you are trying to use a picture as background image for your iPad (wallpaper for the Lock screen or Home screens). In this cases, since the iPad will stretch the image to fit both width or height (depending on screen orientation), which means that your image should have at least one side -height or width- of 1024 pixels. Ideally, any graphic file or photo you want to use as wallpaper on your iPad should be a square of 1024 by 1024 pixels. This will ensure that no image resizing occurs, which tends to make the content of the picture blurry and pixelated, and that the full image will fill your iPad's display regardless of its current orientation (portrait or landscape).