Given two magnets, Gilbert knew that magnetic poles can attract or repel, depending on polarity. In addition, however, ordinary iron is always attracted to a magnet--even soft iron, which loses all its magnetism again when it is removed again.
Gilbert guessed, correctly, that near a permanent magnet such iron became a temporary magnet, of a polarity suitable for attraction. That is, the end of an iron bar stuck to an S pole of a magnet (south-seeking pole) temporarily becomes an N-pole. Because magnetic poles always come in matched pairs, the other end of the bar temporarily becomes an S-pole, and can in its turn attract more iron.
You see this if you dip (say) a horseshoe magnet into a cup with iron pins. As expected. many pins will stick to the poles, but in addition, some more pins will stick to those pins. Yet when the pins are pulled loose, they all are seen to be non-magnetic again.
Gilbert confirmed his guess of temporary ("induced") magnetism by an original experiment (see drawing). Using strings, he hung two parallel iron bars above the pole of a terrella, and noted that they repelled each other. Under the influence of the terrella, each became a temporary magnet with the same polarities, and the temporary poles of each bar repelled those of the other one.