Adding a mesh is fraught with danger! Depending upon the active mode, Blender allows you to add a mesh as its own object in object mode, or in edit mode to add the same mesh as part of another object. If a mesh is added in object mode, there are ate least two ways to delete it: find the object in the outliner window, select it, and using the context menu, delete it, or select the object in the 3D viewport, and delete it there using one of the means to delete objects in the 3D viewport.
On the other hand, if the mesh was added in edit mode by mistake, it is a bit harder. Then you have to select the object, click into edit mode, select an element of the mesh you want to delete, either a vertex, edge, or face, expand the selection to the whole of the mesh (one way is by pressing the key combination CTRL-L), and deleting the selected vertices.
One other factor to complicate matters further: if you added an a mesh in object mode, and delete the vertices in edit mode as described above, you delete the vertices, but not the object, so in object mode you will still see the object's location, even though if there are no vertices to form a mesh.