SAP ABAP Reports are written in ABAP code and generally present specifc SAP data to the user so that they can view, change or download it for use in separate application. The most popular way to create abap reports is to use the alv functionality either view the ALV function modules or the ALV method calls. See here for more information about SAP ALV including example ABAP code.
Another option for building reports within SAP is to use the Adhoc SAP Query and quickviewer to generate yor reports
ABAP reports don't just display data to a user, depending on the capabilities of the ABAPer they can also perform complicated calculations, ftp data, email data, update tables etc etc
BALVBT01
Testprogram ALV: Block list
salv_admin_test_run_reports
SAP ALV test reports
SHOWCOLO
Show different colours available for SAP reports
SHOWICON
Show different icons available for SAP reports
SAP Reports by Module Area
Also see SAP function modules for available SAP function modules
ALV SAP Reports
There are also many ABAP ALV reports available within your SAP system created to demonstrate the various capabilities of Advanced list viewer reports from drag and drop functionality to cell editing and even HTML. Here are a few examples but you can find many more be search for ALV or BCALV.
SALV_DEMO_TABLE_EVENTS
Demonstration of Event Programming using SALV_TABLE
BCALV_BDS_DISPLAY
Show BDS and graphic (in ALV context only)
BCALV_DND_01 ..04
Drag ALV Row to Tree Folder
BCALV_EDIT_01 ..09
Switch on and off the ready-for-input status of the entire grid
BCALV_GRID_01 ...11
Processing Print Events
BCALV_TREE_01
ALV Tree Control: Build Up the Hierarchy Tree
BCALV_GRID_DEMO
Simple ALV Control Call Demo Program
BCALV_GRID_DND_TREE
ALV Grid: Drag and Drop with ALV Tree
Also see further example code published to help you get started and build the perfect ALV report from the following websites
ALV reports and tutorials from GURU99
ALV basics for all types of ALV from
ERPWorkbench