Sequencing: Programming a series of notes to trigger samples or synthesizers. MIDI is the most common standard for sequencing.
MIDI: Musical Instrument Digital Interface; A standardized musical data format created as a solution to the problems caused by early velocity-controlled-pitch based synthesizers and to make every musical piece of technology able to communicate. MIDI is the standard way DAWs and MIDI controllers interact. MIDI data itself produces no sound, only information about when notes start and end, articulation information and other data about the individual channels and song. The data must be passed to a sampler or synthesizer to produce the note information it contains.
Quantize: Quantization is the action of snapping data or values to its nearest integer or otherwise value. You can quantize recorded MIDI data to the nearest 1/16th note for example. Digital audio is usually quantized to 16-bit or 24-bit values while it is being sampled (recorded). As the value of digital audio is changed slightly as it is rounded to the nearest step a 'quantization error' is introduced. This error degrades the signal slightly, but usually inaudibly unless low bit depths are being used.
Bit Depth: The bit depth of digital audio is the number of bits required to numerically identify (in binary) each quantization step used to record the audio. 16-bit audio has 65336 possible quantization values for each sample. The higher the bit depth is the lower the average quantization error will be when the audio is sampled. 16-bit and 24-bit are the most commonly used bit depths in modern recording. 20-bit is pointless to record on computers as data is stored as bytes which contain 8 individual bits, meaning a 20-bit sample takes up the same storage space as a 24-bit word but sounds worse.
Sample Rate: A 'sample' in this context refers to a single value of a digital audio stream. The sample rate of audio is how many times a second there is a new audio sample being replayed or recorded. Audio data recorded with a sample rate 48kHz must be replayed at the same sample rate or it will be altered in pitch and speed. You can 're-sample' audio to a different sample rate but this inevitably degrades the signal slightly. The sample rate is also the highest frequency it is possible to store in the data. The sample rate of CD is 44.1kHz.
There you go, all the boring technical ones done. If you want me to specify anything better just ask. Just basic overviews.
EDIT: Here's my one for DAW, I've never heard anyone say that you NEED to be able to record audio for it to count as a DAW. You just need a way of processing it/editing it. All reason does is process audio samples, but i'd still count it as a DAW. I've produced music with it alone, you can't say it doesn't do what it says on the DAW tin.
DAW: Digital Audio Workstation; A DAW is any program that allows you to record and edit/process audio data, or create audio by sequencing to trigger samplers and synthesizers. Some programs specialize their workflow to recording or sequencing. Common DAWs include Pro Tools, Logic, Cubase and FL Studio.