Trimmed means that the 'junk data' at the end (in hex it is 00's or FF's, essentially blank space) is removed.
A ROM (Read-Only Memory, the retail cart) is always sized to a power of 2: 2/4/8/16/32/64/128/256/1024/2048 Megabits and any unused space is filled with the 00's or FF's mentioned above. When it is dumped, a perfect copy will have that 'junk data'.
For the most part it is useless, and modern trimmers like NDSTokoyTrim will remove it safely.
"Independent" is the release group/person who dumped the ROM or uploaded it to the internet.
A few of the more common ones are Trashman, Bahamut, and Xenophobia (who uses intros making their ROM dumps NOT clean).