Regarding Lenz's Law presented in hyperphycsics The following diagram is presented in hyperphysics as an introduction of Faraday's Law and Lenz's Law.
If the red arrows represent the direction of current, then what do the positive and negative poles across the resistor means? From my understanding, resistors do not produce a potential difference therefore poles shouldn't be present in the first place.

 A: It seems you got confused by the drawing about what is cause
and what is effect.
Of course the resistor does not produce the voltage.
The voltage is produced by the coil.
And this voltage is then consumed by the resistor.
For reducing confusion let us first consider the situation without the resistor.

The changing magnetic field $\frac{\Delta B}{\Delta t}$ produces,
according to Faraday's law, a voltage between the two ends of the coiled wire
$$V=-NA\frac{\Delta B}{\Delta t}$$
where $N$ is the number of turns of the coil, and $A$ is
the area enclosed by one turn.
There is no current flowing, because the resistance
between the open ends of the coiled wire is infinite.
You could measure this voltage by connecting a volt-meter
to the two ends of the coil.
You will find the voltage has a polarity as shown
by the $+$ and $-$ in the drawing.
And there is still no current flowing, because the volt-meter
has a very high (ideally an infinitely high) resistance.
Now let us add the resistor (with resistance $R$).

The resistor reacts to the given voltage $V$ by letting
a current $I=\frac{V}{R}$ pass through the resistor from $+$ to $-$,
i.e. in the direction shown by the red arrow.
This current $I$ produces a magnetic field $\color{red}{B_\text{induced}}$
of its own. And according to Lenz's law it
is directed opposite to $\color{blue}{\Delta B}$.
A: 
From my understanding, resistors do not produce a potential difference

Whenever there is a current $I$ through a resistor with resistance $R$, there is a potential drop $V$ across the resistor equal to $V=IR$. The potential gradient is always opposite the direction of the (conventional) current. This is why in the diagrams the current is moving from + to -. If you were to put the ends voltmeter at those locations in the diagram you would find the signs of your readings to match the diagram.
The diagram is not showing "permanent poles" that are inherent to the resistors themselves. The signs are dependent on the current itself.
