The knife was made by Remington before WWII. The handles are green glitter celluloid, a material akin to what collectors call "Christmas Tree" celluloid. The knife has the acorn shield which is correct for a knife with a punch. It looks like the punch may still have some of the bluing on the inside, which is always nice since it is an indicator of wear on the knife. Originally, the knife would have had an etch on the front of the master reading "Remington" and something else, if you look closely at the blade there might still be some trace of that etch that can be made out in the right light.
One of the most important things about the knife that can't be determined from photographs is what collectors call "walk and talk". That has to do with how tight the springs are. To determine that, the first thing to do is to open the blades a little bit and see if they snap back into place when you release them. Next, move them almost to the fully open position and see if they snap into the fully open position by themselves. There may be a spot at the half open position where they also snap into the half open position, if they do, this is called "half-stops". Many collectors are sticklers for collecting only knives that have good walk and talk. The "talk" refers to the clicking noise the knife makes when snapping into the various positions.
There is a lot information that could be given regarding the knife, however, most newbies are actually only interested in one thing, "How much is it worth?". For the answer to that question, the questions about walk and talk and any etch need to be answered first, if the walk and talk is good and there is some etch remaining an R3415 in the condition shown (I would call it excellent depending on walk and talk) is probably worth between $50 - 100 on the big auction site (eBay). It's actually a fairly common Remington knife. Of course, I am assuming that there are no cracks that I can't see in the handles, or, for that matter, any other damage.
The best way to estimate value is to look up completed auctions on eBay.
Nice knife
P.S. I just noticed that you posted a picture showing a partial etch, a definite plus.
No pattern number on the back of the tang?
Can you post the other side of the knife with the blades open?
