scikit-learn: High / low value for C in SVM
The loss function in SVM consists of both Classification error and Margin error.

Now C is constant that attaches itself to the classification error as given below:

SVM_Error = C*Classfication Error + Margin Error


So, the high value of C means that classification error will be more than the marginal error and therefore model will focus on classifying all the data points accurately. Conversely, if the low value of C means that marginal error will be more than the classification error and therefore model will focus creating the larger margin for the hyperplane