Deductive arguments are arguments in which the truth of the premises is intended to guarantee the truth of the conclusion. For example:
1. All men are mortals
2. John is a man
C. Therefore John is a mortal
Since both 1 & 2 are true, C must be true. For a deductive argument to be good or "sound" it must have true premises and the form must flow logically (validity). Validity is somewhat complex so I won't go into that.
Inductive arguments are those in which the premises are intended not to guarantee the conclusion, but to raise the probability of the conclusion, or give good reason to believe the conclusion. It is based on observation and from this we can form rules of relationships. For example:
1. Humankind has never seen a flying elephant.
C. Therefore elephants do not fly.
Judges mainly use inductive reasoning.