How does a resister "slow down the edge"?

Not at all a dumb question but given that RuggedCircuits described how it does it in reply #4, well ....

Anyway it does it because of the combination of resistance and the capacitance in the tracks an on the input to the device. This is known as stray capacitance and is always present in every practical circuit. The combination of a series resistor and capacitor to ground forms a low pass filter. A perfect edge, that is a change from one logic level to another, consists of an infinite number of harmonics or frequencies. If those harmonics don't go all the way up to infinity but stop short (as all practical circuits will) then the edge can't be perfect and therefore the edge has a finite rise time. The resistor and stray capacitance form a filter that limits the number of harmonics in the edge more than it normally would be, and so the rise time is longer than it normally would be. The bigger the resistance or large the capacitance the slower the edge rises.

All digital components need the rise time on the edges to be a minimum value, this varies considerably so see the data sheet on the component you have in mind.

An SD card with it's socket is a particularly rich source of stray capacitance and cheap memory in SD cards sometimes do not have the specification you would hope for.