Time is the dimension of music, likewise width and height are the dimensions of pictures. When transmitting MIDI data on a wire, events don't need to be marked with time labels, because the time simply flows. MIDI is a real-time protocol. When the events are stored on data structures, like SMF (MIDI files), the events must be timestamped. In SMF, each event has a delta-time, the elapsed time since the previous event, measured in ticks. The time formats on SMF closely resembles the conventions used by the written music tradition, the musical score.
crotchets per minute. MM=60 means 60 crotchets in one minute, or one crotchet equal to one second. The crotchet, also known as quarter note, is the double in length of a half, and the half is the double of a whole. Conversely, the half of a crotchet is an eighth, and this is the double of a sixteenth. These figures are the time lengths of the musical notes, and they are relative measures. Music is written in terms of relative times.
In SMF, the time is measured in ticks. The division value, which is declared into the file header, is the number of ticks in a quarter note. Common division values are 96, 120, 240, 384, 960. The numbers are usually divisible by 3 and 4, and big enough to avoid decimal numbers when measuring the length of very short notes.
Tempo changes are SMF meta-events. They may happen at any point in the time line and are represented in microseconds per quarter note. This magnitude is inverted with regarding to the usual metronome units (quarters per minute), because it can be represented by integer instead of decimal numbers. for instance, mm=60 would be represented as SMF tempo=10000000, and mm=120 as tempo=500000.
As note start and length properties are represented by relative magnitudes instead of absolute times, and tempo changes are flexible enough to be placed at arbitrary points, it is easy to modify them without collateral effects. If you insert a tempo change in a SMF using a MIDI editor software, you don't need to change the length or the starting time of the following or previous notes. Of course, when the SMF is finally rendered to be listened, the sequencer engine needs to do all the time calculations. But not so fast, wait a minute!
When you play MIDI files, it is a common requirement to perform slower or faster than the nominal tempo changes encoded into the file. It is like zooming in picture viewers. For instance, a student may need to render a piece half or slightly slower than it normally plays, or a dancer may need it a bit faster. The ALSA sequencer engine provides a very handy mechanism for programs to do this: the time skew property. You can enjoy this vary-speed functionality in KMid2 and KMidimon, when it is used to play MIDI files.