Support Vector Machine (SVM) is a machine learning model for supervised data classification. SVMs essentially learn a hyper-plane which separates the data space into 2 regions (in 2 class case). In your case, suppose you have images of snakes and cats and you need to classify them. The steps you'll need to follow are
Extract 'features' from the images.
These 'features' may be functions of appearance of snake/cat in your case e.g colour of the animal, shape of the animal etc. By concatenating these features you can get a multi-dimensional feature vector.
Train an SVM classifier
Training essentially learns a separating hyper-plane between the feature vectors of snake class and cat class . For example, if your feature vector is 2-dimensional, training an SVM classifier would amount to 'learning' a line which best separates your labeled-data/training-data.
You could use any of the multitude of freely available libraries of machine learning. In case you speak python, you could use sklearn for the task.
This task of learning (hyper-plane in linear SVM) is referred to training.
Classify the images.
Once you have trained your model, you could then use it classify images whose class is not known.
Note: I am simplifying a lot of details/issues involved in this answer. I suggest you should read-up about SVM
