In general, expressions for validation rules and computed fields are translated into JavaScript and evaluated in the client browser. For validation of data entry, the user gets immediate feedback on the new data.
Some expressions have to be evaluated on the server. This might be because the evaluation involves all the rows, rather than data on the current page only, or because the expression does not translate into JavaScript.
If an expression includes these functions, it will be evaluated on the server:
Aggregation functions, like Sum, Max, Average, First
Case function
External functions
If you use an aggregation function in a computed field, the value is computed on the server and displayed on the client. If the user edits data, the value is not updated. If an action occurs that reloads the page, the value is computed again based on the changed data.