Utilitarianism is one of those rare moral theories that sounds obviously right at first and obviously monstrous a few seconds later. The basic claim: actions are good to the degree they produce happiness (or reduce suffering) — not just for you, but for everyone affected, weighted equally.
This is radical. It says your child's broken arm doesn't count more than a stranger's broken arm. It says you should give until giving more would hurt you more than it would help the recipient. Peter Singer's version (effective altruism) takes this seriously enough to make people uncomfortable: if you can save a drowning child at small cost to yourself, you must; if you can save a stranger across the world with a charitable donation, the moral logic is the same.
Critics push back hard. Bernard Williams pointed out that utilitarianism asks you to be a happiness-calculating machine in situations where having integrity, loyalty, or love would require you to refuse. Other critics note the famous "utility monster" problem: if one being could derive enormous pleasure from harming others, would utilitarianism endorse the harm? Most utilitarians deny this — but the burden of working out exactly why is heavy.