It is about taking the apples looking the most like an apple, the oranges looking the most like an orange, and telling how apples and oranges should be looking like. Those are the farther red and green points from the line separating the two categories.
The Support Vectors, the points supporting the whole algorithm, have equal distance from the line in the middle. They are the apples looking the most like an orange, and the oranges looking the most like an apple.
Support Vector Machines are about assigning examples to a category. The more an item looks like an apple, the more its probability to be an apple, not an orange.
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