Suppose, for example, there is a kind of data that cannot be separated using a single line as shown in this diagram:
Consider these shapes to be different types of data. As you can see, we won't be able to separate a cluster of data by just drawing a single line between them. But the same job of differentiating can be done easily if a complex curve, such as a circle, is drawn instead of a line, just as in the diagram.
The main task of an SVM is to transform original data from this complex space to another space where the function that separates the data points is much simpler. This task is known as the kernel transformation.