Child-directed language can support language learning, but how? We addressed two questions: (1) how caregivers prosodically modulated their speech as a function of word familiarity (known or unknown to the child) and accessibility of referent (visually present or absent from the immediate environment); (2) whether such modulations affect children's unknown word learning and vocabulary development. We used data from 38 English-speaking caregivers (from the ECOLANG corpus) talking about toys (both known and unknown to their children aged 3-4 years) both when the toys are present and when absent. We analyzed prosodic dimensions (i.e., speaking rate, pitch and intensity) of caregivers' productions of 6529 toy labels. We found that unknown labels were spoken with significantly slower speaking rate, wider pitch and intensity range than known labels, especially in the first mentions, suggesting that caregivers adjust their prosody based on children's lexical knowledge. Moreover, caregivers used slower speaking rate and larger intensity range to mark the first mentions of toys that were physically absent. After the first mentions, they talked about the referents louder with higher mean pitch when toys were present than when toys were absent. Crucially, caregivers' mean pitch of unknown words and the degree of mean pitch modulation for unknown words relative to known words (pitch ratio) predicted children's immediate word learning and vocabulary size 1 year later. In conclusion, caregivers modify their prosody when the learning situation is more demanding for children, and these helpful modulations assist children in word learning.