Do I need a Godox master flash to use a TT685-N off-camera?

A simple slave flash (like you can use with a photocell trigger) will just fire in manual mode (with fixed strength) and will require you to use a triggering flash also in manual mode or at least in autothyristor mode: digital camera TTL metering works with a pre-flash, and that pre-flash will already trigger the slave flash prematurely, messing up the TTL metering without actually firing again for the main flash.

The next complex version of slave flash will only fire with the second flash it sees: that works with most built-in camera flashes, still requires the slave flash to be in manual mode and requires you to manually dial in flash exposure compensation because the TTL pre-flash will not get to see the effect of the slave flash.

Then there are manufacturer-specific slave flash protocols: those communicate with short bursts of very short very fast flashes: those allow for the slave flash to work in auto or even TTL mode by listening to the proposals of the master flash. Those protocols are complex and different for each manufacturer.

I'm planning to buy a Godox TT685-N. But I want to use it only as a slave flash. I'm trying to understand if I need another Godox flash to be the master or if my current Nikon SB-900 will trigger it.

You do not need another Godox flash to fire the TT685-N off-camera. It can be triggered by several different methods, and only one requires another Godox unit.

"Smart" optical CLS triggering

Your SB-900 (or, if you're shooting a D7x00 or higher end body with a pop-up flash, your pop-up flash) can be used on-camera as a "smart" optical Creative Lighting System (CLS) commander unit, and the TT685-N can be used as a CLS optical slave. This system allows for full control over the off-camera light, with TTL, HSS, and power/group/ratio control. The horizontal lightning bolt button on the right cycles a TT685-N through five different syncing modes:

• on-camera use (green backlight, no icon)
• CLS commander (green backlight, lightning bolt icon)
• CLS slave (orange backlight, lightning bolt icon)
• Godox radio master (green backlight, antenna icon)
• Godox radio slave (orange backlight, antenna icon)

"Dumb" optical S1/S2 triggering

The TT685-N can also, in on-camera syncing mode, be set with the S1/S2 button, to either S1 or S2 "dumb" optical slave mode. This is similar to the SU-4 mode on Nikon speedlights, where any regular (non-CLS) flash burst can remotely fire the flash. But there's no setting communication, TTL, or HSS. S1 will fire on the first burst it sees; S2 on the second burst (to allow for a TTL metering preflash of the master unit).

Godox radio triggering

This is the method that requires another Godox unit.

Neither CLS nor S1/S2 are the preferred method for remotely controlling a TT685-N, because they are optical. Light signals work well in studio conditions where the ambient light level is low, and there are lots of bounce surfaces. Outdoors on location in bright sunlight, optical can lose a lot of range and reliability, and line-of-sight restrictions (the sensor has to "see" the master burst) can become much more stringent. Most prefer to use Godox system's built-in radio triggering system instead. To use the radio signalling, you do need another Godox unit, either another speedlight or a dedicated transmitter unit, like the X2T-N or XPro-N, which will give you more features.