You can always draw a line through the points, but it isn't always a good approximation. If the points are inherently bunched around a line, then a line through them will approximate them well. If they're a big random cloud, then the line won't. It's the exact same way in ML, except the points are in n-dimensional space and "line" is replaced by "higher-dimensional curve or manifold". Sometimes (e.g. in image processing), the n-dimensional points are inherently bunched around a curve or manifold of the form you're using, and then ML works great. There's nothing deeper going on!