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A dark frame is an image of the same duration and temperature as the light frame taken with the CCD imager with the lens cap on. This image contains a "map" of the dark signal across the surface of the chip. During processing, the dark frame is subtracted from the light frame using software to remove the dark current signal. This is one of the easiest ways to improve your images. If there is one piece of advice to follow: take and subtract dark frames! Your images will show the improvement. To improve your images, and especially if you are doing photometry, you should take many darks and then average them together.
A bias frame is an image, taken again with the lens cap on, for a 0 second duration and at the same temperature as the light frame. This is a "map" or record of the bias signal and can be removed by subtracting it from the final light frame image and its dark frame during processing. This is a very subtle image maipulation and really only becomes necessary when doing high precision photometry. Note that the bias is also used to scale your darks for different integration times.
This is an image taken through the optical system at an evenly illuminated neutral white light panel or source. This information is then divided out of the final light frame to remove the effects of uneven chip sensitivity often caused by such things as the chip itself, optical path vignetting, and the like. If you do photometry, flats are essential. Take 30 or more flats which will then be averaged together to improve results. Some software, like MaxImDL, will allow you to use the same library of darks and biases to process the flats. Yes, flats also need to have darks subtracted! Also, if you use filters, you must take a series of flats through each filter you intend to use that evening. Also you need to take your flats at the same temperature as the imaging session.