Really, there's two kinds of data in cognitive science, information (the data used by the cognitive systems we're interested in), and experimental data (and similar, such as correlational data), which we collect and analyse to try and better understand cognition.
It sounds like your question is about information, so I'll focus on that, but please correct me if that's not what you meant.
The Computational Approach
Most cognitive scientists, from the 1960s onwards, explicitly or implicitly accept what's referred to as the "computational theory of mind", which says the purpose of a brain, or any other cognitive system, is to processes information, in much the same way as a computer does. From this point of view your "data" are neural representations of just what you talk about in computer science, with patterns of neural activation representing logical symbolic states, which are manipulated.
An extremely influential counterpart to this "brain as computer" approach is the the Connectionist, or "parallel distributed processing" approach.
Here, the brain still represents information in patterns of neural activation,
but rather than using "symbols" as you would in a digital computer,
sub-symbollic features of the world around us are represented by
various overlapping patterns across nodes of neurons,
in a way first proposed by McCulloch and Pits (1943), but developed hugely since then,
and "data" constitutes various combinations of these different feature node.
Dynamical, Embodied, Situated (and beyond) approaches
As a final note, a completely different approach to cognitive science, the "dynamical approach", argues that the brain is best seen as a complex, non-linear dynamical system, with a state (pattern of firing neurons) that is constantly evolving through exposure to
the environment, and complex recurrent feedback loops (Spivey and Dale, 2004 give a good introduction to this).
When looked at this way, the brain doesn't deal with discrete "data" (which, remember, is the plural of "datum"), but rather represents the world as continuous patterns of neural activation, connections between neurons and patterns.
Extending this notion, it has been argued, and shown experimentally, that information defined this way goes beyond what's in the brain: we can store and manipulate data using our bodies ("embodied cognition"), and even our immediate environment (situated cognition, see Hutchins, 1995, for an excellent discussion of this in the context of flying a plane). Finally, although I can't remember where, I have seen studies that claim that the same can be said for our clothes, giving rise to "enclothed cognition".