What are 's called?

It is an informal contraction:

An informal type of contraction occurs frequently in speech and writing, in which a syllable is substituted by an apostrophe and/or other mode of elision, e.g., can't for "cannot", won't for "will not". Such contractions are often either negations with not or combinations of pronouns with auxiliary verbs, e.g., I'll for "I will". At least one study has sought to analyze the category of negative informal contractions as the attachment of an inflectional suffix.