Total Beginner,
If you engage LVL CHANGE the plane climbs at whatever speed you have dialled in the window on the MCP.
If you engage V/S the plane climbs at the rate of V/S you have selected. If you have selected say 1000ft/min rate of climb and 240kts, the aircraft will climb at 1000ft/min.
The speed of the aircraft is then dependant upon how much thrust is available at that rate of climb. In a 737 a 1000ft/min rate of climb at 240 kts (low altitude) is easily acheivable and there will be an excess of thrust available. Therefore, the throttles will retard until the thrust commanded is being delivered to maintain 240kts.
However, if you selected say a 5000ft/min rate of climb at 240kts, there might not be enough thrust available to reach this speed, at this rate of climb. The speed will then bleed off and if left uncorrected the aircraft will stall.
With the AP engaged the stall protection system kicks in (on the NG anyway, never flown the classic) and you will get a mode reversion to LVL CHANGE