MIDI instruments and sequences can be thought of like an old player piano. The sequence is the roll of paper, punched with numerous holes, each one representing a note and its duration. The instrument is the piano itself, dormant until the roll of notes tells it what to play, as well as controlling when it starts and stops. Sequencers hold these patterns of notes and transmit them to the instrument in the correct order.
MIDI notes contain much more information than just pitch and duration; they're also capable of carrying parameters that dictate the more subtle expression features that synthesizers and virtual instruments can create. The velocity parameter changes the timbre of each note, altering the volume and tonal properties. Modern synthesizers use multiple layers of samples for each note, mimicking instruments played either firmly or gently. For instance, guitar notes, struck very firmly, would include the simulated rattle of the strings on the frets. Brass and woodwind instruments have an independent "Breath Control" value that can mimic the variety of pressure levels a player can apply to the reed.
Sequencers handle the routing duties for all the instruments connected to them, sending the relevant note patterns to the correct instruments. Instruments can play multiple note patterns at once, for instance, separate left- and right-hand note sequences for a piano piece. The same pattern can also be routed to multiple instruments simultaneously, which you might use to create harmonies on different string sections within a virtual orchestra.
In a system that uses a variety of different instruments and pieces of equipment to play a single piece of music, timing is critical. Pulsing effects and drum machines depend on perfect split-second timing. Memory buffers and data bottlenecks can result in de-synchronization, known in music technology terms as "Latency." To rectify this, most hardware synthesizers allow their internal clock to be overridden by an external source. By synchronizing all of the clock signals to one "Master" pulse, controlled by the sequencer, all the separate components will stay perfectly in sync.