mmimadi:
Hello,
I am trying to wrap my head around mosfets and there is something I just dont understand.
I am looking at this mosfet: http://aosmd.com/res/data_sheets/AO4484.pdf
It has a VGS of +/- 20V and a VGS(th) of 1.7-3v.
I understand that VGS(th) needs a max of 3v to open up the gate.
Wrong. The threshold voltage is where the device switches fully off. In other words below the threshold there is no channel at all (the gate voltage induces a channel between source and drain via electric field).
However to be fully conducting the gate voltage needs to be much higher, so that the channel is fully formed and low resistance. Typically this is at 3 times the threshold voltage.
- What is the VGS rating of 20v for? What if I exceed 3v on the gate?
Absolutel maximum rating, exceed it and the device may instantly be destroyed
- What is the difference between VGS and VGS(th)?
Vgs simply means the voltage between gate and source, Vgs(thr) is the threshold gate-source voltage
- Will PWM duty cycle on an Arduino reflect the voltage on the gate? What is the voltage range on the pwm pins on an Arduino?
No, a PWM signal is a logic signal, its either high or low, nowhere inbetween (well not for more than about a nanosecond during transitions).
- Can I used this as a logic level mosfet? I want to drive 4 amps at 20v from an arduino nano.
Definitely not from that Vthr rating. However it does have a Rds(on) rating for Vgs=4.5V, so it definitely is a logic-level FET. I suspect the Vthr value is nonsense, a misprint (they do happen in datasheets!). Its probably more like 1.5V in reality.
Thank you so much for helping me clarify. Ive been researching for a few hours and im stuck. 
Anyway, ignore the threshold voltage, its not useful. The Rds(on) ratings quote a Vgs value - those are the one's to use for switching. Typically a logic level MOSFET has a 4.5V Vgs entry for Rds(on), and only a 10V one if not logic-level.