It's an alternative way to organize your provinces. As a general rule, either you put them in a state or a trade company (you can also leave provinces as territorial cores so they have very little benefits but use less governing capacity. Only provinces outside of the super-region your capital is in can be added to a trade company. These super-region borders do not exactly conform to those of trade nodes, but as Russia you should want to trade company every node downstream of Kazan and Astrakhan (Samarkand, Persia, Siberia, Girin, Yumen etc.). IIRC there's one area in the Siberia node still in Eastern Europe so you state that one, and trade company the rest.
As for what effect this has, I can explain it by the book as the wiki does, or try to explain it in a more practical manner:
- Provinces in a trade company have significantly increased provincial trade power. This gives you more leverage in contested nodes.
- Provinces in a trade company have severely reduced contributions to tax, manpower and land force limit. They also have a minor reduction in production income but both the former and the latter can be mitigated partly through trade company investments. Overall though, they WILL make you more money, don't worry about the tax loss.
- Trade company provinces have no penalties from wrong culture or religion. For Russia there's lots of Tengri and Sunni provinces you can conquer that are better to put in a trade company than trying to convert.
- You gain an extra merchant for every trade company you have at least 51% provincial trade power in. This really lets you chain a massive trade network.
- Trade companies can be invested in on an area basis (so a group of provinces that can also be a state) and also have a few investments where you can get one per node that can give effects on a national level and/or the whole node. These are extremely powerful!
As for how this is relevant to your Russia, here's some things you should be doing for your trade situation.
- Re-organize your merchants. You got the ones transferring from Kiev and Kazan right, the one collecting in Baltic is acceptable but you're misusing the ones collecting in Astrakhan and Novgorod. The one in Astrakhan should be steering trade, and the one in Novgorod should be moved to either Siberia or Crimea to also steer trade.
- Consolidate the trade nodes downstream of Novgorod. You have many more provinces you should be taking from Commonwealth in the Kiev node, and a couple in the Crimea node. Conquer Nogai, Uzbek, Oirat. Push out the Ottomans! They should be well below the Caucasus. Not only is it a danger to you, they're eating your lunch trade wise! Crimea and Astrakhan are nodes YOU should be dominating.
- Trade company everything south and east of the Eastern Europe super-region. Great parts of the world can potentially flow into Novgorod if you get to work! Build your own silk road. You already fully own Kazan, into this node you can get trade from Astrakhan. You'll want to fully own Astrakhan too, into this node you can get trade from Persia and Samarkand. If you fully own Samarkand, you can get trade from Yumen. If you fully own Yumen... you can bring in trade from all of China.