Explain in layman's terms Vgs and Vgs(th) of MOSFET's
Vgs is just the voltage from gate to source (with the red lead of the multimeter on the gate and the black one on the source). Everything else is from context. 

The Absolute Maximum Vgs is the maximum voltage you should ever subject the MOSFET to under any conditions (stay well away). Usually the actual breakdown is quite a bit different (borrowing from this datasheet):



Vgs(th) is the voltage at which the MOSFET will 'turn on' to some degree (usually not very well turned on). For example, it might be 2V minimum and 4V maximum for a drain current of 0.25mA at Tj = 25°C (the die itself is at 25°C).. That means that if you want your 20A MOSFET to really turn on fully (not just conducting 250uA) you need a lot more voltage than 4V to be sure about it, but if your Vgs is well under about 2V you can be pretty sure it's well turned off (at least around room temperature). 

Rds(on) is always measured at a specified Vgs. For example, it might be 77m\$\Omega\$ with Vgs = 10V and Id = 17A and Tj = 25°C. That 10V is the Vgs you need to feed your MOSFET for it to be happily turned on so it looks like a very low resistance.  

Vgs also comes up when you want to know the gate leakage. Igss might be +/-100nA at Vgs = +/-20V and Tj = 25°C.