Terminology for the use of datasets as data points As computers are getting bigger better and faster, the concept of what constitutes a single datum is changing.  

For example, in the world of pen-and-paper, we might take readings of temperature over time and obtain a time-series in which an individual datum is a time, temperature pair.  However, it is now common to desire classifications of entire time-series, in the context of which our entire temperature time-series would be but a single data point in a data set consisting of a great number of separate time-series.  In image processing, an (x,y,c) triple is not a datum, but a whole grid of such values is a single datum.  With lidar data and all manner of other fields things that were previously considered a dataset are now best thought of as a datum.

What is the term for datasets that are themselves composed of datasets?  The term "metadata" is occupied, I should think.  Are there any papers that talk about this transition from datasets of data to datasets of datasets and what the implications are for data scientists and researchers?
I don't think that this is anything new. Let's use your example of classifying an entire time series, say predicting word 1 vs word 2 for speech recognition. We can write out the data as a data frame like we would do with any other multivariate data: observations at time 1, time 2, etc as the predictors and the classification label as the response variable.

Each observation is a vector of the values at particular times for your subject, plus the label--no different than any other multivariate data. Sure, there might be special dependence structure because of the time series nature of your data, but you can still write it as a multivariate problem.

Okay, let's say that you hit the speech signal with a wavelet transform, resulting in an image-looking spectrogram of 2D data. Then just consider each "pixel" (time-frequency pair) to be a variable in your multivariate problem, along with the classification label. This is some kind of bijection between an $m\times n$ matrix and $\mathbb{R}^{n\times m}$.

You can extend this idea to 3D or 4D data (or higher), too. Just unwrap the high-dimension tensor in some kind of map $T^{m\times n \times \dots} \rightarrow \mathbb{R}^{m\times n \times \dots}$.