Graph editor stuck with multiple keyframes

There is nothing at all wrong with your graph displays. You are just editing the value graphs. If you want one line you need to edit the speed graph. Please consult the User Guide. Please type graph editor in the Search Help field in the top right corner of After Effects and read up on the UI and the options. Please take a look at my tutorial. Please describe exactly what you are trying to animate and how it is supposed to look. 

If you are having problems following a specific tutorial, send us a link. 

You have chosen to edit and view the value graph of a property like the Position or Anchor Point of a layer that has two values in the array. Change the layer to 3D and look at the position graph and you will see three lines. The line color corresponds to the axis color for the property, Red is X, Green is Y. and Blue is for Z. If your graph is for Layer/Transform/Position it is telling me that the layer stays in the same X position and moves down, then up in Y.  You cropped the screenshot so this graph could be for any property with two values in the array. It could just as easily be for Layer/Transform/Scale or Layer/Effect/Lens Flare/Flare Center. When posting a screenshot, please don't crop it so we know what you are talking about.

If you change the Graph Editor options to edit the Speed graph or you pick a property with only one value like rotation, you will only have one line. 

Maybe this tutorial I did on using the graph editor will help. It's almost impossible to make a predictable adjustment to the motion path of any property if you try and edit the value graph. It's much easier to edit the motion path of a layer using the pen tool in the Comp panel and then control the timing using the speed graph.