8-bit, 16-bit, 24-bit
This refers to the amount of information stored for each pixel on your screen. For an 8-bit display, this amounts to a string of eight 1's or 0's, yielding 256 different possible numbers (i.e. 256 different colors can be displayed at the same time). 16-bits yields ~64,000; 24-bit: 16.7 million.
This term is borrowed from signal processing, and describes when a function is undersampled, yielding unwanted results. For example, drawing a diagonal line on a low-resolution raster display, yields an undesirable "staircase" look.
Alpha refers to the opacity of a pixel. The alpha channel was invented by graphics researchers at Lucasfilm, and has become the standard technique for compositing. The standard alpha channel is 8-bits, or 256 levels of opacity. Note: Photoshop tends to describe alpha differently, and hints that any channel in an image that is not R, G, or B, is an alpha channel.
Real world images are continuous and have no discrete units, whereas computer displays use discrete areas of information (pixels). To summarize an image as a series of discrete samples is to discretize it.
Since a majority of graphics displays are still 8-bit (and can only display 256 colors simultaneously), special techniques are needed to display images with many more colors present. Dithering simulates additional colors by juxtaposing two different colors to imply a new one. An extreme example of dithering is the display of early Macintoshes, which approximated levels of grays by clusters of small black and white dots.
To interpolate is to insert values in between. This is frequently used in the context of estimating intermediate values of an unknown function where discrete values are known.
Fairly self-explanatory, lossy/lossless describes the character of a compression algorithm. Lossless algorithms concentrate on how to compact data without losing any information. Lossy algorithms concentrate on how to remove data that is less critical to human perception.
A raster display is one that is made up of a grid of pixels (contrast this with now-extinct vector displays which displayed graphics by tracing them like a pen -- think Asteroids). Rasterization is frequently used in the context of converting vector-based graphics (e.g. Illustrator, PostScript files) into pixel-based graphics (e.g. TIFF's, GIF's). Effective rasterization relies on antialiasing.
table entry
The GIF format, like many 8-bit computer displays, is based on indexed-color. Indexed-color can be thought of as a digital paint-by-number scheme. Whereas RGB images work by storing a grid of numbers representing amounts of red, green, and blue, indexed-color stores at each pixel a number (for 8-bit, between 0 and 255). That number is used to index into a separate listing of what-number-is-what-color (a color table). Tricks like color-cycling screensavers, and real-time brightness/contrast adjustment use indexed-color: the data in the image are kept constant, and only the table entries are changed.

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