In Support Vector Machines (SVM), the margin is the distance between the hyperplane and the closest data points. A hard margin is used when the data is linearly separable, and we dont want any misclassifications. In this case, the SVM tries to find the hyperplane that separates the two classes with the maximum margin possible. However, when the data is not linearly separable, or we want to allow some misclassifications, we can opt for a soft margin. In this case, the SVM tries to find the hyperplane that separates the two classes with the maximum margin possible while allowing some misclassifications.

In hard margin SVM, the objective function is just the regularization term, which is the square of the norm of the weight vector. There is no loss function in this case.

In summary, a hard margin is a margin used in SVM when the data is linearly separable, and we dont want any misclassifications.