When you press the plunger down, it forces air into the drain and increases the atmospheric pressure on it. If the item is dislodged, the pressurized air is free to travel throughout the rest of the piping. When you then pull back up on the plunger, the vacuum created will force anything inside the tube to be forced upwards.
Boyle's law is:
$$
p_1 V_1=p_2 V_2\\
1 = \text{plunger not depressed}\\
2 = \text{plunger depressed}
$$
If the item does NOT get dislodged:
The $p_2$ (pressure after the plunger is pressed down) must increase since the volume that the air can take up decreases by forcing down the plunger. When it is pulled back up, the volume can then increase and the pressure decreases.
If the item DOES get dislodged:
The $V_2$ will increase greatly because the air is now free to move throughout the entire pipe. The $p_2$ is subsequently lowered. We now have:
$$
p_3 V_3=p_4 V_4\\
3 = \text{plunger depressed}\\
4 = \text{plunger not depressed}
$$
Now the rest state is the plunger depressed. When we decompress the plunger, we gain volume and the pressure then falls.
Does this make sense to you?