As documented under Optimizing UPDATE Statements:
Another way to get fast updates is to delay updates and then do many updates in a row later. Performing multiple updates together is much quicker than doing one at a time if you lock the table.
You may also find the page on Optimizing INSERT Statements helpful and informative.
To summarise, in the most general terms: connecting once and sending a single UPDATE statement is better than connecting once and sending multiple UPDATE statements, which in turn is better than connecting multiple times to send a single UPDATE statement on each connection.
Beyond that, there are a host of techniques that can be harnessed to optimise further—but we would need to know the specific configuration and requirements at hand.