What does the term "slow drift" mean?
Drift in general refers to a parameter that changes slowly.  In this case, the parameter is the input offset voltage of the opamp.  A ideal opamp amplifies the voltage difference between the positive and negative inputs:

Out = Gain(Pin - Nin)

Real opamps have a little error in when they see the positive and negative inputs being equal:

Out = Gain(Pin - Nin + Err)

This error value can drift over time and temperature, which is what the paper was referring to.

Note that this offset voltage results in a DC output error.  A step change in (Pin-Nin) will still result in the same size output step.  This property is the basis for chopper stabilized amplifiers.  Basically the input voltage is fed in as a sequence of steps, and the resulting amplitude of the step changes used at the output.  Any slowly varying DC offset on those steps is therefore ignored.

In cases where your signal doesn't contain DC (like audio), a simple high pass filter will remove the offset.  Since the offset changes (drifts) very slowly, it can be thought of as very low frequency noise on the signal.  If the lowest meaningful frequency of your signal is well above that, then a high pass filter removes the DC drift.