An internal DSL (often called an Embedded DSL) is a DomainSpecificLanguage that is written inside an existing host language. It's a common way of thinking in a number of programming language communities - particularly the Lisp community. It's now gaining a lot of attention as DSLs are a common way of thinking in the rapidly growing Ruby community.
When people talk about internal DSLs I see two styles: internal minilanguages and language enhancements.
An internal minilanguage is really using an internal DSL to do the same thing as you would with an external DSL. You consciously decide to use a subset of the full GPL for a minilanguage section of your program. It might look something like this (example from my Language Workbench paper)
mapping('SVCL', ServiceCall) do extract 4..18, 'customer_name' extract 19..23, 'customer_ID' extract 24..27, 'call_type_code' extract 28..35, 'date_of_call_string' end mapping('USGE', Usage) do extract 9..22, 'customer_name' extract 4..8, 'customer_ID' extract 30..30, 'cycle' extract 31..36, 'read_date' end
This is all valid ruby, but its use of a subset of ruby makes it seem almost like a custom DSL.
Unlike an external DSL you are limited by the syntax and programming model of your host language, but you don't need to bother with building a parser. You're also able to use the host language features in complicated cases should you need to.
The alternative way of using internal DSLs is quite different to anything you might do with an external DSL. This is where you are using DSL techniques to enhance the host language. A good example of this is many of the facilities of Ruby on Rails. Look at these bits of Rails validation
validates_numericality_of :age validates_uniqueness_of :ssn validates_format_of :length, :with => /^\d+(in|cm)/
Reading these bits of Rails's validation, it looks like we've given the ruby language new keywords. Of course we haven't modified ruby, this is all clever metaprogramming. But it feels like we've enhanced the ruby language.
These are both very useful techniques. As with any classification there's a fuzzy line between them (Rake could be thought of either way.)