Why do some free-standing ice makers need floor drains?
Most commercial-grade ice makers don't maintain freezing temperatures in the actual ice bin; the ice itself keeps the temperature cold in the bin, and the refrigerator coil then only has to freeze the ice tray. This strategy has several advantages:


The "cold" side of the refrigeration coil can be placed inside the bin, right against the tray, so it makes ice faster than your "frost-free" kitchen freezer icemaker, without needing to be defrosted (because it doesn't have to maintain freezing temperatures, it defrosts itself automatically between batches).
The coil and overall refrigeration system is thus more efficient at what it does (making ice quickly).
The ice is easier to scoop as it doesn't melt and refreeze when exposed to the bin door opening and closing.
The ice is "warm ice" which, again, won't try to refreeze after it melts in your drink (forming that big ice ball you get from cubes or crushed ice from your kitchen freezer.)


But, the downside is that the ice is continually melting and must be replaced with new ice, and the melting water has to be drained. Commercially, the amount of water lost to melting is usually pretty low because the ice is consumed relatively fast, but there is some and it does have to go somewhere. Your kitchen freezer, at about 0*F, can maintain hard frozen ice indefinitely, so it doesn't need a drain and it only has to replace the ice at the rate it's used, which is a good thing because the ice tray relies on ambient air temperature to freeze the water, instead of active transport of heat by the clooling loop in contact with the tray. Similar "home-grade" ice makers are smaller in size and keep the ice frozen. These are good for the occasional large party, but they just don't make ice fast enough for a drink station at a restaurant or concessions stand.

As far as placement, the drain line can pretty much be anywhere and go anywhere, as long as it goes into the sanitary sewer and obeys all other code regarding slope, length to the nearest vent stack, etc. There is a big difference between your basement floor drain and the one in a professional kitchen; the one in your basement was designed to drain relatively clean water either from a plumbing failure or from weeping through the basement walls. It ties into the municipal storm sewer, an "open" sewer designed for precipitation, which will dump any water you put in it directly to the nearest creek. Professional kitchen floor drains tie into the sanitary line, which is the "sealed" sewer that carries food and bodily wastes and cleanser residues from most of your interior drains out to the wastewater treatment plant where those wastes are removed. So, if you buy an ice maker that needs a floor drain, you will need to have a drain specially installed that feeds into the sanitary line. The design is pretty standard; a 3 or 4-inch line, with or without a grate over it, that drops straight down about a foot into a J-trap, and from there to the main sanitary trunk line. This drain will need a backflow preventer on it.