How does one then interpret kernel density distributions with values greater
than one?  

My output from the density function.  
---
density(delt.m[[1]][,6], na.rm=TRUE)

Call:
        density.default(x = delt.m[[1]][, 6], na.rm = TRUE)

Data: delt.m[[1]][, 6] (171 obs.);      Bandwidth 'bw' = 0.004501

       x                  y           
 Min.   :-0.05211   Min.   : 0.00586  
 1st Qu.:-0.02177   1st Qu.: 0.43632  
 Median : 0.00856   Median : 3.08833  
 Mean   : 0.00856   Mean   : 8.23366  
 3rd Qu.: 0.03889   3rd Qu.:14.97542  
 Max.   : 0.06923   Max.   :30.04107
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