ArcMap supplies us with the Spatial Join tool, but there is another way to join data by location. This is very helpful when one wants to have one layer display spatial information from a second layer. For example, you have a California "Counties" layer. You also have a polygon layer for populated areas of California. But you want to change the "Counties" layer's symbology to show relative area or number of national forests inside each county. So you need the "Counties" layer's attribute table to include a field that has the sum of the area of populated place polygons and a sum of the total number of populated place polygons in each county. Still following?
Right click on a feature in the table of contents, click "Join...," and then change the first option to "join data from another layer based on spatial location." Then you can choose to calculate the sum, average, etc. of one layer's field (populated place's population field, shape area field) that spatially is contained in the second layer (counties, in this example). Now the Counties layer contains a field that displays the sum of a field from the Populated Places layer. Pretty sweet.
Tip: if you simply want a count of how many features of one layer are contained in the feature of another layer, just add a short integer field to the first layer in which each feature has a value of one. Then when you calculate the sum, the new field in the second layer will show how many features from the first layer are contained with the fields of the second layer.
Here is a link to ESRI's ArcGIS Help 10.2 page (Joining data by location (spatially) is in the middle of the page):
ArcGIS Help 10.2: About joining and relating tables
The following map supplies an example (Archaeological sites contained in USGS grid quadrangles):
I also wanted to display the relation of site density to supervisor district, so I clipped the USGS Grid layer based on the Supervisor Districts. Then I had to merge the 5 USGS Grid layers back together because I wanted the "Graduated Colors" "Quantities" Symbology to cover the entire county, and didn't want the Natural Breaks skewed from district to district.

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