Trackers, in the context of music production, are pieces of software designed to leverage the full capability of early sound hardware. If you're familiar with how tile maps work in video games, it's a similar concept. A limited pool of samples or sound channels can be mangled and manipulated at an extremely granular level through commands. As such, songs aren't a linear audio file but a sequence of commands that the hardware executes in real time.
This is efficient in terms of memory usage since the data of the song is code rather than audio. They were therefore used extensively in early video games and in the <90s demo scene. There are countless trackers available today ranging from authentic (see FastTracker or MilkyTracker) to modern takes (see Renoise)
The world of handheld trackers is more limited. From my perspective there are three pillars of the handheld tracker world:
1: LSDJ. A homebrew piece of software that runs on the original Gameboy released in the early 2000s. Often considered to the best way to compose music for the Gameboy.
2: LGPT (piggy). Lesser heard of but deserving of more love in my opinion and my favourite. Originally designed in the mid 2000s for hardware akin to and including the Sony PSP. Was abondoned by the original creator but forked in recent years by a Swedish developer to whom I'm eternally grateful. Deals exclusively with 16-bit samples
3: Dirtywave M8. If you're into synths you've probably come across the M8 even if you're not aware of it's lineage. A passion project by a single person. Likely the best value for money standalone piece of music gear you can buy, although that's like saying "the ChatGPT user with the best critical thinking skills". The two concepts don't really go hand in hand. It will run you around 600 simoleons. Didn't stop me from picing one up though
If you've ever heard the below sound before, you've trackers to thank for that.