Induction refers to the change in the electric or magnetic state of a system caused by proximity to (being near to, but not necessarily in contact with) an electrically charged or magnetized object.
Electric induction (also called electrostatic induction) is the separation or rearrangement of charges that occurs when one object is brought near to another object with a net charge (or a part of another object with a net charge).
This is why a charged balloon will cling to an uncharged wall.
Magnetic induction (also called magnetostatic induction) is the alignment of atomic dipoles that occurs when one object is brought near to another object with a net magnetization (i.e., a magnet).
This is why refrigerator magnets (which are permanent magnets) stick to refrigerator doors (which become temporary magnets).
Electromagnetic induction is the creation of an electromotive force (i.e., a voltage) that occurs when a conductor is moved through a magnetic field in such a way that it "cuts" the magnetic field lines. (The word "cuts" here appears in quotes since magnetic field lines always form closed loops and cannot actually be cut.)
This is how coil of wire rotating between opposite magnetic poles can be used to generate electric current (i.e., this is how a generator works).
