Basically, it shows emphasis. Imagine a child boasting about going to a party that her brother wasn’t allowed to attend. James isn’t going, but I am. In English, she’d put emphasis on the word I. She’d say “I” louder and with more emphasis because she’s boasting.
In Irish, the same would be rendered instead with the suffix -se.
Níl Séamus ag dul ann, ach táimse.
There’s no need to say the new word (táimse) with extra emphasis as in English, the suffix itself does the job in Irish.