What do each of the three SVM classes in R represent? Inspired by this post, I took a look at this doc

SVN in R output this:

Statistics by Class:

                     Class: 1 Class: 2 Class: 3
Sensitivity            1.0000   0.9412   1.0000
Specificity            1.0000   1.0000   0.9762
Pos Pred Value         1.0000   1.0000   0.9796
Neg Pred Value         1.0000   0.9865   1.0000
Prevalence             0.2778   0.1889   0.5333
Detection Rate         0.2778   0.1778   0.5333
Detection Prevalence   0.2778   0.1778   0.5444
Balanced Accuracy      1.0000   0.9706   0.9881


What are each of the three classes?
Go to the kaggle site that you shared. 
Click on Data on the left. Click on datadict.txt. This is known as data dictionary, a file that help us understand the dataset.


We can see

23: outcome 
- what eventually happened to the horse? 
- possible values: 
1 = lived 
2 = died 
3 = was euthanized 


Those are the meaning of the $3$ classes. You might also like to print out hodata$outcome or do str(hodata$outcome).