If you look through something with a fine pattern on it, at something with a fine pattern on it, the two patterns may interfere and show a moiré pattern. Take, for example, some muslin cloth and a brick wall and try it for yourself. But the sensor of your digital camera is a fine pattern of light-capturing cells, and if you use it to capture something with a fine pattern there is a danger that the resulting image will show the moiré pattern that isn’t really there.
Now, the nice folk that design digital cameras really don’t want them making pictures with things in them that aren’t really there, so in front of the sensor they put a device called an anti-aliasing filter. This filter scatters – blurs – slightly the light, enough to stop moiré being captured in most cases. This is good, as it is very difficult to properly remove moiré in post-processing. But it is also bad, as it means your digital images will never be quite as sharp as film images of the same scene.
This is why you should ALWAYS sharpen your photos before letting anyone see them, as the sharpening process makes them look more like film, though it can’t restore the fine detail that is lost in the blurring process.
You may have noticed that some camera manufacturers have introduced versions of their high-end cameras with the anti-aliasing filter removed – and of course are charging more for the privilege. What is happening is that as the pixel count is going up, and the pixel spacing is decreasing, so the cases where the image source will interfere with the sensor to produce moiré are fewer. They are most likely to occur in fashion or architectural photography – things with fine patterns in them – so the manufacturers are offering a choice of cameras without the filters for those that work in landscape, nature etc. In practice, of course, unless your lenses (and technique) are really top of the range you may not see the difference.
Shirt photo from http://canoncanada.custhelp.com/app/answers/detail/a_id/2269/~/the-moire-effect