What does stick fixed and stick free longitudinal stability mean in simple terms?
Trim the aircraft. Do a "doublet" (means stick forward and back to the trimmed position for a short moment, or rudder deflected and neutral again) to upset the trimmed state.

Now watch the response while you keep all control surfaces at their trim position, making sure the control surfaces don't move when the aircraft goes through its motions. This is quite easy on GA aircraft and big aircraft with powered controls (if you do this on an Airbus, switch it to direct law).

Next, repeat the maneuver but let go of the stick respectively the pedals. Watch how the stick or pedal position moves with angle of attack respectively sideslip changes: This is your control surface floating freely. Again, watch the response. Normally, it will now take longer for the resulting oscillation to die down and the oscillation frequency should be slightly lower.

The first is the fixed-stick aircraft stability, the second the stick-free stability. Normally, stick-free stability is lower and proportional to the stick forces when flying away from the trim point. The difference between both is determined by the hinge moment coefficients of the control surface. For the elevator the floating angle $\eta_f$ is
$$\eta_f = -\frac{c_{r0}+c_{r\alpha}\cdot\alpha}{c_{r\eta}}$$

with $c_{r\alpha}$ the hinge moment coefficient over angle of attack $\alpha$ and $c_{r\eta}$ the hinge moment coefficient over control deflection. Both coefficients are normally negative and the absolute value of $c_{r\eta}$ is larger that that of $c_{r\alpha}$. When $c_{r\alpha}$ is zero, both stabilities are equal because the floating angle is zero.

Another way to study stick-fixed pitch stability is to trim the aircraft at two different speeds or load factors and to measure the trim change necessary between trimmed state 1 and trimmed state 2. The result is the speed stability rsp. the maneuver stability.

Stick-free stability is only relevant in case of manual controls. FBW aircraft only exhibit stick-fixed stability except for the very unusual case that the control surface actuators are overpowered by the aerodynamic forces.