Aggregated Measures are any measure that has calculated over multiple rows of the data in the database. So the difference between 1000 in sales for a Day vs 1000 in sales for a specific record. Aggregation is often disabled when creating a scatter chart (You want to see all of the sales event rows in one view - not aggregated). Aggregating Data describes this option.
Variable size Bins are bins that have been manually defined. Bill Lyons creates an example calculation called [Group] in the post - Create variable size bin in tableau as an example. Srinidhi Narayan also shows this off within his correct answer here - Create custom bins
Binned Dimensions created by the bin feature of Tableau will be based upon a a value supplied to the calculation and then divided over the values - Follow along in the online help here - http://onlinehelp.tableau.com/current/pro/desktop/en-us/help.html#calculations_bins.html?Highlight=bins
I hope that helps.
Non aggregated measures are just the individual row data - this page in our help gives a good description (it's all the way at the bottom) Aggregations
Variable Sized Bins are basically bins that aren't the same size as each other. In our automatic bin function:Create Bins from a Continuous Measure the bins will all be the same size as each other. If you need variable sized bins, you would generally create a calculated field like:
[Age] < 21 THEN "Under 21"
[Age] <= 32 THEN "21-32"
[Age] <= 42 THEN "33-42"
[Age] <= 52 THEN "43-52"
[Age] <= 64 THEN "53-64"
hope this helps!