The Innateness theory is based around the idea that children have the capability to acquire their first language naturally and easily. The theory was made popular by linguists such as Noam Chomsky who believed that children had an innate capacity to acquire their first language via a cognitive phenomena that he called 'a Language Acquisition Device' or LAD. This meant that children were born preloaded with linguistic rules that allowed language to be acquired quickly and easily.
For evidence, Chomsky points to children's creativity with language and how they seem to have an understanding of grammatical rules from a young age. For example, a child may say 'i gived it to her'. We know that the correct form would be ' i gave it to her' but the mistake the child has made is an overapplication of the rule for past tense verbs. With regular verbs, adding -ed as a suffix would indicate past tense but as gave is not a regular verb they made the mistake, but their understanding of the rule is correct. Chomsky would say that this is evidence of the LAD, as grammatical rules such as these would be too complicated and would take far longer to learn by interaction with adults and exposure to the language alone, so as a result children must have an innate capacity to acquire language.