Imagine you're driving down the road, and trying to stay in a lane. Neither your car nor the lane is perfect, so you occasionally have to nudge the steering wheel to keep between the lines.
As long as you're just nudging the steering wheel, you're fine. But imagine now that your steering wheel was so sensitive that the smallest push you give it would turn the wheels too far. You drift a little right, so you turn the wheel left, but instead of returning to the middle you go too far. You're now too far left, so you turn the wheel right, but you push it too hard so you go even further to the right. Now you're further to the right, so you push it even harder to the left. And so on, until your car either crashes into the guardrails or flips.
This analogy describes, more or less, how a proportional controller works. A well-tuned proportional controller drives the system towards a desired setpoint, like the car between the lane lines. A poorly-tuned proportional controller (with \$K_P\$ too large) drives the system too hard, creating growing oscillations around a setpoint until the system either oscillates between maximum values, or explodes. In other words: the control system is making the system unstable.
As for your schematic: the LRC system you've posted has no active components, and will never go unstable. No matter what components you choose for L, R, and C, for any bounded input you'll have a bounded output. It is, at worst, marginally-stable when R = 0 (which never happens in reality). You can prove this by deriving the differential equation for this system, and proving its bounded-input-bounded-output (BIBO) stability, by either confirming that the limit of the impulse response at \$t=\infty\$ is finite, or by taking the Laplace transform of the differential equation and evaluating it at \$s=0\$.