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If you put "o" near predicate, it means you are emphasising it. You emphasise "he/she"

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Now you emphasise they.

 I would have translated this in English as:

Lit: first s/he put her/his plate on the table.

Free: s/he was the first to put her/his plate on the table.

(note: it is tabağını - his or her plate, not just a plate or dish).

As the others have said, the "o" emphasises he/she as being the first.

without it, I would have translated it into English as:

First, s/he put her/his plate on the table.

With the "o" it means there were a numebr of people who put their plates on the table, but this person was first.

Without the "o", this person went on to do other things, but first they put their plate on the table.

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