Support Vector Machines (SVM) are supervised learning models that are very popular in the realm of machine learning. SVMs are really good at analyzing labeled data and detecting patterns. Given a bunch of data points and the associated labels, SVMs will build the separating hyperplanes in the best possible way.
Wait a minute, what are "hyperplanes"? To understand that, let's consider the following figure:
As you can see, the points are being separated by line boundaries that are equidistant from the points. This is easy to visualize in 2 dimensions. If it were in 3 dimensions, the separators would be planes. When we build features for images, the length of the feature vectors is usually in the six-digit range. So, when we go to such a high dimensional space, the equivalent of "lines" would be hyperplanes. Once the hyperplanes are formulated, we use this mathematical model to classify unknown data, based on where it falls on this map.
There is something called the kernel trick that we use in SVMs. Consider the following image:
As we can see, we cannot draw a simple straight line to separate the red points from the blue points. Coming up with a nice curvy boundary that will satisfy all the points is prohibitively expensive. SVMs are really good at drawing "straight lines". So, what's our answer here? The good thing about SVMs is that they can draw these "straight lines" in any number of dimensions. So technically, if you project these points into a high dimensional space, where they can separated by a simple hyperplane, SVMs will come up with an exact boundary. Once we have that boundary, we can project it back to the original space. The projection of this hyperplane on our original lower dimensional space looks curvy, as we can see in the next figure:
The topic of SVMs is really deep and we will not be able to discuss it in detail here. If you are really interested, there is a ton of material available online. You can go through a simple tutorial to understand it better.