Transformers are controls in the ASP.NET V2 portal framework that allow you to connect web parts that expose incompatable endpoints.
The ASP.NET V2 control-set exposes two standard transformers - RowToFieldTransformer and RowToParametersTransformer.
These baked-in transformers allow your web part connections to work automatically for parts that are dealing with IWebPartRow on the provider side and either IWebPartField, or IWebPartParameters on the consumer side.
It therefore makes quite a bit of sense to use these interfaces when writing your own web part controls for added extensibility. For example, if you are exposing your connection endpoints based on a custom interface then what are the chances that a third-party web part vendor would implement that interface? None right? But the chances that they would be implementing one of the standard interfaces are quite high. So, by deduction, if you are not using those standard interfaces then your parts will probably never be able to work with third-party web parts.
Transformers expose a piece of custom user interface that allow you to manage the property mapping between the connection provider and the connection consumer. As an example, you may have an AddressWebPart that exposes a row of data with the following column definitions:
{Street1, Street2, City, State, Postcode, Country}
And a WeatherWebPart that consumes the following data:
{Country, Region}
In this case your AddressWebPart would expose data based on IWebPartRow and the WeatherWebPart would consumer data based on IWebPartParameters (because it is more than one field).
Because of these endpoints, the ASP.NET framework "just knows" that they can be connected using the RowToParametersTransformer to assist with the configuration mapping. When you are configuring the transformer, you would use the custom user interface provided by it to map the columns from AddressWebPart to the correct parameters on the WeatherWebPart:
{Country -> Country}
{State -> Region}