Let's say I just want to plot a xy curve or something similar. For the example let's say that the data is:
x y
-1 2
0 1
1 2
2 5
3 10
How does the concept of "measures" and "dimensions" come into play here? I just want to plot this on a 2d coordinate system. Do these both become 'dimensions' then, or how would that even work?
Dimensions and Measures come into play when you are using Tableau to view aggregate results.
That is, you want to combine groups of data records that share common values - such as the same month, location, product type, manager etc, and then report an aggregate value that summarizes all the individual values for each group of records -- such as the sum, average, min, max etc.
The fields or expressions used to determine which records will be grouped together are known as dimensions. You can think of them as how you choose to segment or partition your data, and they often follow the words "per", "by" or "for each" in an English description of your analysis. The choice of dimensions thus determines the level of detail (or aggregation) for the visualization.
The fields or expressions used to compute the aggregate values, along with the selected aggregation function, are known as measures. You can think of them as the statistic that you are measuring. So SUM(Sales), AVG(Profit), MAX(Temperature) are examples of measures. Sales, without an aggregation function, is just a field.
You may notice some similarity to the SQL Group By clause. That is not an accident.
Note that a field can be treated as a dimension in some circumstances and a measure in others. The choice you make in the data pane in the left margin is just the default behavior.
Finally, to answer your question, if you aren't performing aggregation and want to view individual data records, then you can turn off Aggregate Measures for a worksheet from the Analysis menu. In that case, Tableau will not issue aggregate queries and the concept of dimensions and measures does not apply. That is useful if you want to plot each value say in a scientific diagram or a map of individual locations.