A spline can be either a line or a surface that is shaped by moving a small number of "control" points. The rules are pretty much the same for both spline lines and spline surfaces. The idea is to use the least number of points to control the shape because that will save calculation. Think of the points as similar to the strings that control a puppet. Envision a line with a some strings attached to it every few inches. When you pull the end of one of these strings, the line bends at the point where the string is attached. If you pull another string it bends in that direction. So splines are lines or surfaces whose shape is controlled by the positions of a small number of points in space.(in our case these points are the ends of the strings you are pulling)
Suppose there are two pieces of string attached to the line about an inch from each other. If you pull one of the strings, it has the greatest affect at the point where it is attached, just as the other string has its greatest affect at its attachment point. However, you can see that both strings have "some" affect on each other's points of attachment. This is the underlying principle of the spline. The closer the point to the "control", the stronger the influence of the "control." Yet each control point/string has "some" influence on points further away. The further away, the less the influence until it gets so far away it has no influence.
In order to identify the points on the line, the first point (at the start end) is called 0 and the last point on the line is called 1. So each point on the line is somewhere between 0 and 1 inclusive. These values are called the parameter. We can identify any point on the line as a decimal value 0 to 1. Now, this is where you meet a critical concept. Pay attention to the fact that this line can be bent every which way, but no matter how it is bent, a point always keeps its position on the line.. so the point at 0.5 is always at 0.5 no matter how the line is twisted by the control points. This is the rule. It sounds almost too simple. But if you lose track of it you can get lost quick. So keep it clearly in your mind as we go on. Think of it this way. If you had a rope and you marked it at the 3/4 point (0.75), no matter how you tie the rope in knots, that point is still 3/4ths of the way up the rope.
Making a spline involves learning the rules that say where the control points should be attached to the line and how much influence each control point has on the line and on the neighboring points on the line. i.e. it describes how much overlap each control point has with the other control points in influencing the position of a point on the line.
Easy to say, but how is it done. As always, the devil is in the details.
It is best to start with spline curves (lines) to get a feel for how they work, and later move on to spline patches (surfaces.) This is the traditional approach for teaching splines because all the conceptual stuff is the same. It is easier to demonstrate the principles with a line than with a surface, and once the ideas are clear, going to a surface is a trivial matter.