What is meant by direct, routed and proxy mode on a gatekeeper?
There are up to four modes that H.323 gatekeepers can operate in; not all gatekeepers are able to operate in all modes. Check your gatekeeper's manual to find out what modes it supports.

Direct mode
This is the simplest gatekeeper mode where the gatekeeper acts as little more than an address book. After an endpoint has received permission from the gatekeeper to make the call and has received an E.164 address translation, the gatekeeper plays no further part in the call.
Nearly all gatekeepers support this mode. The built-in gatekeeper in the Cisco acquired TANDBERG/ Codian products and Cisco TelePresence Serial Gateway Series products uses only this mode.

H.225-routed mode
As well as performing the functions of a Direct mode gatekeeper, one in H.225-routed mode will act as a proxy for H.225 messages involved in setting up a call. This allows the gatekeeper to control the overall bandwidth used on calls. Many gatekeepers support this mode. The Radvision ECS refers to it as Q.931-routed mode and Polycom PathNavigator as Routed mode.

H.245-routed mode
A gatekeeper in H.245-routed mode will perform the functions of a gatekeeper in H.225-routed mode but will also act as a proxy for H.245 messages involved in media control. Only media packets will pass directly between the endpoints. In addition to the benefits of H.225 routed mode, this allows the gatekeeper to control the video and audio codecs in use on a call and to implement flow control. The Cisco VCS and the Cisco acquired TANDBERG Gatekeeper refer to this as Routed mode.

Full proxy mode
A gatekeeper in full proxy mode will route all setup, control and media packets. This offers security benefits because the endpoints cannot discover each others' identities, and can be used for firewall traversal. Many gatekeepers do not support this mode due to the amount of processing required.

The Cisco VCS's interworked mode allows calls to be made between an H.323 device and a SIP participant. In this scenario, it operates in full proxy mode. Similarly, if a Cisco VCS or Cisco acquired TANDBERG Gatekeeper is performing H.460 firewall traversal it will be using full proxy mode; in either case the call will require a traversal license. In full proxy mode, the VCS also performs IP version traversal.