Statement:
Reviewing the definition of inductance, I found the following definition from Wikipedia:

Question
Can someone explain to me how change in current will induce an electromotive force (one that will oppose the present current)? And what is meant by a magnetic field is inductive?

Are you familiar with Lenz's Law? A current in a circuit will produce a magnetic field, so when current is changed, magnetic field is changed, and a changing magnetic field will induce an EMF that opposes the change. If I'm not mistaken, this is what people refer to as "back-EMF" in circuits.

See the right-hand grip rule which relates current direction through a conductor to magnetic field orientation. Induced EMF will be in opposition to the current flow.