The most widespread use of positive contractions, at least in the English language, use a pronoun such as he, she or they, combined with affirmative "be" verbs. An example, "he'll go to the store," is the positive contraction word combination "he'll." The contraction is positive because it affirms an action that will happen in the future.
Often times other nouns -- whether proper or not -- are used to make positive contractions instead of pronouns. For example, the statement "Sam's a happy person" includes the proper noun "Sam" combined to the present tense "be" verb, "is," to create the contraction "Sam's." Again, it's positive because it declares a state of being that occurs in the present.
Sometimes positive contractions use words other than nouns to convey happenings or actualities. For instance, the descriptive declaration "There'll be punch and pie and the party" describes a reality, but employs an adverb instead of a noun. It is still positive because it infers an occurrence that will happen.
The antithesis of a positive contraction is a negative contraction. It is a contraction, but instead of affirming, it negates by combining the word "not" to a part of speech, usually a "be" verb. As an example; the statement "She won't be coming to the party" is negative. The contraction is the word "won't." It is negative because it denies an occurrence.