A real image forms when multiple rays from the same point meet at again at another point. Without optical element, the rays just go in their own different directions and don't meet again. So there is no image.
When you put a convex lens in front of the pen, why you can now see the image of the pen on the paper?
Because a convex lens bends the rays so that the diverging rays originating from any given point on the pen—as long as it is further than the focal point—start to converge on the other side. 538
The basic rules say that a ray passing through the centre of the lens passes straight and a ray passing parallel to the optical axis on one side passes through the focal point.
These rules allow you to trace three different rays through the lens and where they intersect on the other side, there is the real image (which you can see iff it coincides with a piece of paper). You could trace the other rays too, but that requires more advanced analytical geometry.
When then can you see the image of a torch when you shine it on the paper?
I you are talking about a real torch—as in a stick with a piece of burning rag wound around one end—you won't. You'll only see a more brightly illuminated spot where the paper is closer to the torch.
If you are talking about the electric kind, most of them are reflectors, that is they have a parabolic mirror mounted behind the light emitting element.
The mirror should be mounted so that the light emitting element is closer to the mirror than the focal point, in which case there is no real image, but a virtual image behind the mirror. Virtual image can be seen directly if the light is not too bright to look directly into it.
However sometimes the mirror is mounted too far from the light element—or can be positioned there in the variable focus lights—and then there is a real image ahead of the light you can project on a paper. 538