We want to sum over all coalitions where agent i is not present. In this notation it is denoted by F \ {i}.
The interpretation of the Shapley value:
Take a coalition where agent i is not present.
Add agent i and calculate the increase of the coalition value: value of the coalition after agent i joined minus value of the coalition when agent i was not in the coalition. This is agent i's marginal cost/value of joining this coalition.
Multiply this by the specified weight.
Do all these steps for all coalitions where agent i is not present and sum the weighted marginal costs/values: hence the notation you are asking about.
We want to sum over all coalitions where agent i is not present. In this notation it is denoted by F \ {i}.
The interpretation of the Shapley value: