Hi hokhani,
Let's try a slightly different approach. (For all the purists here, a slightly tortured word picture.)
Start by remembering that a voltage is defined as a potential relative to the potential of something else. For instance to use a voltmeter to measure the voltage of a battery you connect the meter leads to the battery terminals. That gives you the voltage, or potential difference, between the two terminals of the battery. If you use only one meter lead, it won't read anything because there is no reference level or charge for the meter to relate to.
And you will get the same Zero reading if you connect both meter leads together and to one battery terminal, in this case because you are trying to measure the same thing you are using as a reference
When you are inside a Faraday cage, the only reference you have is the cage itself. If you try to measure the voltage that you are at, you measure from yourself to the cage; and will read Zero volts. If there is an electric field outside the cage, the entire cage, being conductive, will end up being at some uniform voltage dependent on that external field (and also on whether or not the cage is Grounded, but that can be ignored as the end result is the same). Again if you measure the voltage between you and the cage the result is still Zero, even though the cage itself may be at some crazy high voltage. Once more, that's because the cage is the only reference you have.
Now if you disconnect the meter lead that is connected to the cage and poke it thru a hole in the cage, you will read the voltage Difference between the cage and the end of the meter lead.
If you stick your finger thru that hole in the cage, the end of you finger will be at the voltage of the field at that point, while the rest of you is at the voltage of the cage. If it is a small difference you won't even notice it, above about 50V you will feel it.
All of this boils down to the rule that states: "Everything within a conductive enclosure is at the potential of that enclosure."
Lots of folks here can express a 'Proof' of this mathematically. However, for that you have to both understand the math and understand why it applies; not easy when you are first introduced to it!
Hope this helps.
Cheers,
Tom