It does signal processing in free software. This means you can learn from it, and modify it to do new things. The big idea is to give ordinary software people easy access to 'hack' the electromagnetic spectrum, that is, to understand the radio spectrum and think of clever ways to use it.
GNU Radio offers reconfigurability. Spending $1000 on a piece of radio hardware buys you access to whatever that particular radio is configured for. If you have adequate generic hardware, the radio processing can be done in software. Currently only a few forms of radio are duplicated in GNU Radio software, but if you understand the math of a radio transmission system, you can reconfigure your GNU Radio to receive it.
The GNURadio software is free software, licensed under the GPL, so you can improve on it, tweak it, start a business based on it, and torque it, all without paying anyone or asking anyone's permission.
Radio is that bit of the electromagnetic spectrum that sits between brain waves and daylight.
GNURadio can do cool and scary stuff that old special-purpose radios can't do, like tune in and record every FM radio show, or all the cellular traffic on a certain street corner.
GNURadio provides a library of signal processing primitives and the glue to tie it all together.
The programmer builds a radio by creating a graph (as in graph theory) where the nodes are signal processing primitives and the edges represent the data flow between them.
GNURadio provides primitives that use interprocess communication to transfer chunks of data from the real-time C++ flow graph to Python-land.