'Smart server' is a term used when a server hosting a repository uses its own server software, as opposed to simply sharing files over a standard protocol like HTTP or SFTP.
Some version control systems enforce a client-server model, where software must be running on the system where the repository is located, which the client software accesses.
In Bazaar, the use of server software is optional, not required. The Bazaar client software needs no specific server software running on the system where the repository is located. It can simply access and modify the repository directly as files. This can even happen over a network. For instance, using Bazaar you can access a repository via a normal HTTP or SFTP connection, without the need for any Bazaar-specific software to be running on the other end. In this case the server hosting the repository can therefore be called a 'dumb server' because it needs no software running on it other than the ability to share files.
While this 'serverless' mode of operation allows for far greater flexibility, because the repository may be hosted anywhere without any special software requirements, it can be less efficient, because more requests must be made over the network connection for some operations.
Where network and software policy permits, Bazaar allows you to run a server on a system that hosts the repository using the bzr serve command. A client can then access this server over a network and experience faster and more bandwidth efficient access to the repository for some actions. The extra speed and bandwidth efficiency comes from the fact that the server is intelligent enough to do some repository related processing at its end before sending data across the network, hence it is called a 'smart server'.