I understand it to confirm that the parties signed the above-mentioned on the day and year.
"IN WITNESS of which the parties have set their hands the day and year first before written"
As for the precise meaning, I don't know because either it is obscure legal language, or garbled English. I would expect to read :
IN WITNESS of which the parties have set their hands this Third Day of June, in the year Two Thousand and Seven
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