A relation is what it sounds like. A relation between numbers and/or objects.
A function is just a special type of relationship. In order for a relation to be a function, it must have only one output for one input.
On a graph, the x-axis is the input and the y-axis is the output. If you draw a vertical line through a point on the x-axis and there is only one point on that vertical line, then it is a function.
The only graph that meets these criteria is the first graph.