1. To carry out or perform something.
The soldier refused to execute the order.

2. To complete and give validity to a legal instrument, meaning to sign, seal, or notarize.
All joint tenants will need to execute the instrument.

3. To kill a condemned person according to law. (execution of death sentence)
He is going to be executed because of the murder he committed.
To run an application (program) in computers. The file extension ".exe" in Windows comes from the term "executable".
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