Terminal services gateway is a new feature included in Windows Server 2008 under the Terminal Services server role. It allows external client computers to connect to internal resources, such as RDP clients without having to configure port forwarding at the firewall.
A simple example of how I would RDP into a computer located behind a firewall without using TS Gateway:
Open up port 3389 on my firewall and forward it to a computer on my LAN. Then from an external client, I would connect to the computer that I am port forwarding to, and from there I could RDP into other computers as needed.
If I wanted direct access to more then one computer on my LAN, I would have to configure RDP on the "server" computer to listen on a port other then 3389, open that port on my firewall, and port forward.
With TS Gateway, all I need to do is specify the resource and the TS Gateway address, and I can connect (assuming you have setup TS Gateway, authorization lists for computers and users, etc). The connection using RDP over HTTPS and the more common port 443.
So far the only downside to TS Gateway the extra overhead required in setting it up. You must have a server running Windows Server 2008, a certificate for the HTTPS (TLS 1.0), as well as the following roles, RPC over HTTP, IIS 7.0, and Network Policy and Access Services. If you don't have an externally trusted certification, you can create your own, but then the public CA certificate used to sign your cert must be installed on all client computers. If you have a domain, and only domain computers will be connecting, this isn't too much of a problem.