What does 様 Sama mean?

Sama is the honorific one step above さん. It raises the person addressed, and the reason it sounds grander in English than it does in Japanese is that fandom meets it in throne rooms while Japanese meets it at a till.

The character

様 read yō means appearance, manner, or the state something is in, and it keeps that job in ordinary vocabulary describing how matters stand. As an honorific it works by indirection: rather than naming the person, it gestures at their situation, which is a politeness strategy English also uses when it addresses a letter to an office rather than a name.

Where it is actually used

On envelopes, after the recipient's name, as a matter of course. In shops and on trains, where customers and passengers are addressed with it as standard. In the fixed phrase for everybody present, used at the start of announcements. In correspondence to anyone outside one's own organisation.

None of that is deferential in the sense of grovelling. It is the register of commerce and correspondence, and a clerk using it is not making a claim about rank any more than an English shop assistant saying sir is.

Why anime made it sound like a title

Because of who wears it in fiction. Aristocrats, heirs, deities, the head of a household, and anyone a servant character is addressing. Those are the contexts that stick, and they share a quality the everyday uses do not: the gap between the two speakers is enormous and permanent.

From a sample like that, lord is a fair guess. It misses that the same suffix is doing unremarkable work in every convenience store in the country.

The one rule worth knowing

Applying it to oneself is arrogant, and fiction uses that deliberately. A character who refers to themselves with it is signalling something about their own self-regard, and the joke or the menace lands entirely on that.

The exceptions are frozen phrases where the form has stopped meaning anything, which is the usual fate of politeness markers in any language.

What English lacks

English has no attachable honorific that scales. Sir and madam are standalone forms of address and cannot be suffixed to a name; Mr and Ms attach but do not escalate, since there is no more formal version to reach for when the situation demands one.

Japanese has a ladder with several rungs, and the speaker must stand on one of them every time a name is spoken. Chan, kun, san and this are four settings on the same dial, and the choice is never neutral.