In short: Child benefits are state payments, in cash or in kind, that support families during pregnancy, at birth and while raising children; some are paid only below an income limit.
Simply put: Unlike maternity benefit, they are usually not earned through contributions but granted under conditions such as family income or school attendance. Some are one-off (for example at birth), others monthly.
Example: A family with two children checks whether its income per member is below this year's limit. If it is, it applies and budgets the benefit as a separate, less certain income.
General rule: Each country designs its own family benefits; EU coordination rules decide which country pays when family members live or work in different Member States (*).
Example: Bulgaria — the Family Allowances for Children Act provides one-off payments (pregnancy, birth, adoption, twins, children starting first and eighth grade, and others) and monthly ones (up to age one; until completing secondary education, but not after 20; for a child with a permanent disability) (Article 2). They are granted by the local Social Assistance Directorate on an application (Article 10). Amounts and the income limit change each year (*).
Check in your country — The social assistance or family benefits authority: types, amounts and income limits for this year.
Source: Your Europe — Work: https://europa.eu/youreurope/citizens/work/index_en.htm · Social Assistance Agency (Bulgaria): https://asp.government.bg/bg/deynosti/sotsialno-podpomagane/semeyni-pomoshti