Available from Chapter 3 of Final Fantasy VII Remake, Battle Intel Reports have you complete various tasks on behalf of Professor Hojo's intern, Chadley.
Each objective completed allows the young scientist to develop new Materia, many of which will prove to be very useful.
He will also give you access to VR battles against various Summons. Once beaten, he will award you with their relevant Summon Materia.
Notes
The completion of the these objectives is retroactive: you can contribute to their achievement even before Chadley has proposed the task.
For example, if you are tasked with using the Assess Materia on 10 enemies, if you have done this before Chadley gives you the task then that task will automatically be completed.
You'll find Chadley in the main hubs of the game, such as the Sector 7 or Sector 5 Slums. You won't run into him all the time, so go and see him as often as possible before the story progresses.
The Materia he makes is available in limited quantities, so buy his entire stock if you can afford it. This will give you greater scope for customization of your team.
It may not be wise to attempt some VR battles depending on where you are in the main story. Fighting Bahamut when you're only with Cloud and Aerith, for example, is highly discouraged.
List of Battle Intel Reports
Note that all VR battles can be replayed at will, at the difficulty you prefer.
You will not receive EXP from these battles, but you will receive AP. This means they can be a good way to farm Materia levels early on, even if time-consuming.