Whenever you have two conductors in space, you have a transmission line property associated with those conductors.
When the conductors are far apart, the characteristic impedance is high. Which means, if you deliver some amount of voltage or current into the wires, then at the first instant (in this case, say, when the contacts touch), the ratio of voltage to current (which has units of impedance!) equals that impedance.
As time goes on (more specifically, as the wave bounces back and forth along the transmission line -- this takes mere nanoseconds, but is clearly discernible on a fast enough oscilloscope!), the energy in the transmission line is dissipated, and the V/I tends towards the "DC" circuit levels: supply voltage and resistance.
When the conductors are closer together, the characteristic impedance is lower (about 100 ohms, for average twisted pair).
But more importantly, the impedance of each wire, with respect to everything around it -- other test leads, the oscilloscope body, the table, the universe itself -- becomes much higher (that is, less coupling, crosstalk). Which means the signal between the two wires, is that much more confidently just the signal between the wires that you started with, less of the signal itself has leaked away (radiation loss!), and less of any nearby (spurious, interference, noise) signals have snuck in!
FYI, as obtuse as it may seem to introduce transmission lines here, mechanical contacts really do close that fast -- fractions of a nanosecond! It only takes that much time to close the nanoscopic gap between metal surfaces, some tiny fraction of a millimeter (in fact, 10s of nm!), for the gap to go from "nonconducting" to "tunnel current" to "touching". Or if the applied voltage is enough to cause breakdown of the air (10s of V), then the tunnel current (when not quite touching) ionizes air, and a spark jumps, igniting in a similar time frame.
This is why spark sources are so important in the design of electronic devices. It only takes one spark to flip a pin's voltage momentarily! Sure, a spark might not happen very often -- just when someone flips a switch, or a refrigerator cycles on and off, something like that. But in that instant, a surge of electromagnetic radiation is released, and with such high frequency components (100s of MHz to GHz!), it doesn't stay in wires very well (hence, it's important that the wires be routed close together!).
Tim