TSdbi is the base package in a group of packages, that provide a common interface (API) to time series sources and databases. That is, you specify the connection, and after that all of your R code syntax can be the same, and does not depend on the specifics of the underlying mechanism. Many of these packages are wrappers for other packages. The main benefits of the TS* packages are that they provide both a common interface and a mechanism for specifying the time series representation to be returned. Other features include the ability to handle vintages of data (sometimes called "realtime data") and panels of time series.
The package TSdata contains (only) a vignette which is a general guide to all the packages. TSdata is difficult to install because it requires working versions of most of the other packages. It will generally be easier just to get the vignette from the TSdata vignette on CRAN. Of course, that mainly discusses released packages.
Several of the packages pull data from the Internet. This includes TSsdmx, TSmisc, TSjson and some experimental interfaces in TSmisc2. Of these, TSsdmx is the most general mechanism.
Other packages provide a mechanism for building an SQL time series database. This includes TSMySQL, TSPostgreSQL, TSSQLite, TSodbc and untested TSOracle. The package TSsql provides the common sql part of the these packages, while db engine specific details are provided in the individual packages. If you already have a backend SQL database, and are not building the database, just an interface to an existing database, then the TSsql package function TSquery may be useful. It can be used to construct time series from SQL databases that contain sequential data but were built for purposes other than storing time series data. Other than TSquery, functions in TSsql are intended for internal use by the db specific packages.
Some packages act as wrappers to convert the API of existing time series (database) interfaces. These include TSfame, which is a wrapper to the fame R package that is an interface to Fame databases. TSpadi (deprecated) is also a mechanism to interface to Fame and possibly other database.
TScompare provides a way to compare large numbers of series on different databases.
TSdbi uses the NAMESPACE and methods from package DBI.
The general status of the packages is here.