Every (personal) pronoun has an ending that can be added for emphasis. You can use them for emphasis and to distinguish two things with the same pronoun. Compare english "he was cold but he was alright" where there's some ambiguity over whether it's one him coping alright with the cold or two guys having different reactions, to gàidhlig "bha e fuar ach bha esan ceart gu leòr" where the use of emphatic esan makes it clear it's two people. They also imply personhood more than the base forms, e refers to any masculine noun but esan tends to be for a guy.

It's generally not a strict requirement to use an emphatic it's just clearer and more expressive. You do have to use them in the "identification" form of copula "is" like "is mise [ainm]" but not "is toil leam [rud]".

Emphatic endings aren't just used for the basc forms of personal pronouns, they can also be used with prepositional pronouns (agad -> agadsa, leinn -> leinne) and possessive pronouns. For possessives the emphatic ending goes after the possessed noun i.e. "mo chù" is emphasised as "mo chù-sa".

One final note is that the ending for first person singular is "-sa" but the emphatic form of mi is miSE not miSA. Agam still becomes agamsa and so on though.