Generally, the VNAV path extends upwards from the runway, through various waypoints, speed and altitude constraints, deceleration points etc. When you program it, it draws a line based on prevailing conditions.
When you're on the path (in a Boeing at least) you'll see SPD / PATH (AT / pitch).
Any time you aren't on the path, you'll either be SPD / VNAV ALT in level flight (possibly ALT HOLD) or EPR(THR HLD) / VNAV SPD in a descent.
There are two ways to leave the path in descent:
1: move the aircraft from the path by slowing down or speeding up (Speed intervene)
2: move the path away from the aircraft by reprogramming it.
For example, if you delete a speed/alt constraint, VNAV will recalculate for an idle descent to the next constraint instead, which will immediately put you high or low on the new path. Since you're now not on the path anymore you'll default to VNAV SPD in a descent.