trimmed means the rom is in a smaller size. (by cutting out useless empty bits of data in the rom that release groups add so it matches the required scene size)
intro means that there's a intro (from the release group when you load it up.

 

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).

 

I hate intro screens.