For the past few weeks I've been noticing something a bit strange that I haven't noticed before. Whenever I turn on my computer and boot up Windows. Even after I login, I notice that the HDD/SSD activity light remains on constantly for a really long time. Even though I'm not doing anything. It'll stop after maybe 10 or more minutes. I'm kinda paranoid. Is there a way to figure out what application or exactly what is being written/read from my HDD?

The easiest thing is to simply open up Task Manager and sort the list of applications by disk usage. 

The most common culprits in my experience are antivirus software (including and especially Windows Defender) running scans in the background and the Windows Compatibility Telemetry.

Edit: obviously typing whilst skelsey was!

With earlier versions of Windows, the OS wasn't really usable until all of the required bits had been loaded during the start. In an attempt to speed things up, Windows 10 is usable as soon as just the essential bits are loaded but it does mean that data is still being read from the drives for a while after everything seems to be working normally, hence the drive lights keep flashing for a while.

For it to go on for 10 minutes, it could be something like your antivirus updating or scanning. If you open Task Manager (Ctrl/Shift/Esc) and go to the Processes tab, in the CPU column you can see which apps are running and using processor time during the start sequence. If you click on the letters "CPU" at the top of the column, it will put the most active processes at the top. You can also look under the Startup tab to see what runs during startup.

Here's a good writeup on Technet on how to use Task Manager and Resource Monitor (it's written for Windows 7 and 8 but works the same way in 10):

https://answers.microsoft.com/en-us/windows/wiki/windows_8/how-to-use-task-manager-and-resource-monitor-to/79d0e537-6c62-4fcc-866a-ab16c713727c