Not a plumber, but I'm a homeowner and have dabbled in DIY plumbing. If this is a kitchen drain, see if it's an intermittent issue. Plastic pipe joints can leak when they get overly hot (like when you drain pasta water and pour boiling water down the drain). If it's not a constant leak, just run cold water when you are draining very hot water.
The white plastic nut is part of the P trap assembly. The metal pipe is an adapter or nipple. The nipple should be seated against a seal inside the P trap, and the nut tightens them together. In your photo it doesn't look like the nut is threaded on very far, so it can't hurt to give it a turn. But if the nut is broken or the seal is waterlogged, it would need to be replaced.
If the drain isn't in constant use, I'd be inclined to remove it and bring to your home center. Otherwise, this photo would probably be what you need to identify the parts needed. The parts shouldn't be too costly.