Today's activities end here.

Literal

Today [attributive-の] activity [topic-は], with-this closing.

お開き is an auspicious euphemism for 'closing, ending, wrapping up' — specifically used for the end of meetings, parties, and gatherings. The logic is superstitious: 終わる ('to end') sounds finalistic and inauspicious, so 開き (literally 'opening') is used in its place, reframing the end as a fresh opening. これで ('with this') marks the current moment as the closing point. A nice example of lexical taboo avoidance.