I was studying about the Guanella 1:1 balun and came across the term "choking reactance". What does this mean? Why does its value need to be large?
A "Guanella balun" is really just a common-mode choke.
For differential-mode currents, the current on one half of the transmission line is equal but opposite the current on the other half. Likewise, the magnetic fields due to these currents is equal but opposite, so they cancel, and so there's no magnetic field at all. Consequently differential-mode currents see no inductance at all, and pass through as if the choke isn't there at all.
For common-mode currents the magnetic fields don't cancel, and so the choke looks like an inductor. This is the "choking reactance", inductance being a specific case of reactance. Ostensibly, we have the feedline where we don't common mode currents to flow (the "wrong" place), and we have some other place we'd like them to flow (the "right" place). For example in a coax-fed dipole, the "right" place is the leg of the dipole attached to the shield.
The idea with a common-mode choke employed as a balun in this case is to make the impedance seen by the common-mode currents on the feedline significantly higher than the impedance to the "right" place, whatever that is. Consequently most of the current will flow in the "right" place, and very little in the "wrong" place: the feedline.
Here's a similar but much simpler situation at DC:
Since R1 is significantly bigger than R2, almost all of the current will flow through R2. The idea with the choke is similar, except instead of resistances we are using reactances which are analogous for AC.
So in order for this balun to be effective, that impedance seen by common-mode currents, the "choking reactance" due to the transformer, must be significantly higher than the impedance to whatever the other place is where you'd prefer those currents flow.
I'm not familiar with the term "guenella", but:
A choke, in this context, is typically an inductivity with the function of suppressing high frequency signals/noise.
As inductivity, it has inductive reactance. Think of inductive reactance as the "resistance in effect at a specific frequency $f$", i.e. $2 \pi f L$, with $L$ the inductance.
Hence, the higher it is, the higher the resistance of the inductance to the frequency.
In the context of baluns, things might be a bit more complex: Since inductivity is the ability of something to store energy in the magnetic field, and baluns often are pretty much transformers, i.e. devices that convert electrical current to magnetic field change, and back to current, this size is tightly linked to the ability of a transformer to transport energy. I must admit that I'd need a lot more context to explain why its value would need to be large (a.k.a. slight ciriticism: give more background in your question!)