Woodford faucet water leaking out of little holes near hose
Those holes are probably part of the now required anti-backflow feature. There are rubber seals inside that must be replaced.
Shut off the water at the valve in the pic and unscrew the cap on the left. There will be parts inside which must be replaced. Looks like a large Allen wrench fits inside. If you don't want to get a special large Allen wrench, one could probably use a pipe wrench or channel locks.
EDIT  Before you take it apart be sure that the hose you are connecting to it is threaded on correctly and has its own washer seal in place.