What are the 'd' and 't' variables for in Faraday's law of electromagnetic induction (ε equals dΦB/dt)?

t means time, d means "an infinitesimal small" rate of change.

So think of the expression dΦB/dt as ∆ΦB/∆t

Read as "the change of magnetic flux over a change in time"

Except that this "change" is soooooo small that it is nearly, but not equal to 0, at that point, we switch to the notation of dΦB/dt

d is not a variable, it is an operator, operators tell you what to do

this is a notation from calculus, for instance, the notation dx/dt means differentiate the variable x with respect to time (t)

if you are not familiar with the elements of calculus, this may seem pretty mysterious, but is really a pretty simple idea

do this expression does not mean to divide d in the numerator by d in the denominator, but is an instruction of what variable to differentiate

d indicates differentiation. t indicates time.

In other words, ε equals the slope of Φʙ curve when plotted against time.

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d is an operator, and it means "infinitesimal change in the following quantity". The letter d is chosen because of the term differential.

dΦ_B means "infinitesimal change in the quantity named Φ_B, i.e magnetic flux"

dt means "infinitesimal change in the quantity named t, i.e. time"