Term for taking a subset of a time series by selecting one every $n$ values (to get a lower resolution) What is the technical term for creating a new times series via sub-sequence of the indices? 
Or by another method like taking the averages over some window?
The point would be to get a lower resolution time series, like going from hourly to weekly.
 A: There are several terms.
Decimation or, generically, downsampling, is a term for retaining values at regular intervals as used in signal processing literature.  There is a Wikipedia article.
Resampling, including undersampling, is a procedure of removing (or even duplicating) observations to improve the forecasting of rare events.  See Moniz, Branco, and Torgo for a discussion and a Wikipedia article on oversampling and undersampling for brief mentions of some general undersampling techniques.
Thinning is the procedure of randomly removing points from a point process, where the chance of removal typically depends on the time.  See Khoo, Ong, and Biswas for a good description of the connection between point processes and time series as well as of thinning and related procedures.
(Warning: "Binomial thinning" of an integer time series actually is a model, often termed INAR, relating successive values in time.  It's a different procedure.)
Windowed averages appear in so many ways and so many contexts that they have many names: they are basic ingredients of smoothers; they result from mathematical convolution; they have been termed windowed means, rolling means, and (in the spatial statistical literature) focal statistics and block statistics. The fundamental distinctions among them are (1) whether the windows are overlapping or form a disjoint partition of time; (2) what statistic is retained in each window (mean, median, or something else); and (3) whether and to what extent the values may be weighted.  There are so many possibilities for this I can't give you a list of references, but instead encourage searching using these terms as keywords.
A: I think downsampling may be what you are after. Google returns many results for time series downsampling; here's one relevant link to get you started: http://opentsdb.net/docs/build/html/user_guide/query/downsampling.html
