The very short answer is: In many of the same ways. Language, culture, food and religion are most obvious things. A fun exchange was between fish sauce produced on the Italian arcipelago and East Asian produced pasta or noodles.
A quick note: The Silk Road is not a single road spanning from east to west (even though many travel agencies try to capatalise on this miss conception.) It is rather a large network of trade routes spaning from west to east on both land and water. Modern day literature and marketing has painted a romantic picture, where you can take travels along the 'original' road or take the Orient Express to get the fealing of the Silk Road. Not true, mostly just marketing and miss-conceptions
Depending on the timeframe some products were more valued by the Chinese. Then there is the topic as weather you are talking about the land routes and caravans or the route throug the Indian Ocean.
Lets begin with what the Chinese in general didn't want: Weapons. You might know how European produced weapons were one of the main trading objects in the Trans-atlantic trade during the 16th-18th century. You might also have heard the trans-atlantic trade described as a triangular trading route. That was only somewhat true. Most of the trading ended giving a handsome amount of silver or gold (mostly silver).
A lot of the conquest the Spaniards did was with the purpose of getting more silver to trade with. The only thing really the Chinese where interested in was silver. Silver was one of the driving forces for the Atlantic trade, simply to get more valuta to trade with. Weapons had no real trade value in China, as they themself had powder weapons. Most of the products produced in the new World could also be produced in China. What China (and East Asia) really lacked was precious metals. The silver was then traded in for silk, spices, tea etc. Most of the silver found in South America actually ended up in China.
One major development the western world saw but East Asia missed out on was ship development. McNeill and McNeill discuss it and concludes that rivers in South-East Asia are much less favorable, why the caravan development was much more succesfull. Also the mild waters comparativly seen in the Indian Ocean resulted in a lesser need for sturdier and stronger sea faring ships. (The Human Web - A bird's-eye view of world history)
There is one more thing to remember. The earlier we go in the history the chance of the same trades man going all the way from east to west and vice verca becomes less and less. The product that got traded most likely changed hands and got traded with dozens of times. This is especially true before the invention of the large and sturdy ships from the 16th century and up. The caravans never really started off in Marakesh f.x. and traveled all the way to China. It got sold and bought several times throught its travel time. This form of trade has a lot smaller impact of and empire or part of the world, culture wise, than a direct link between a trading post and the homeland. That is also why you see far less trading of languages outside of the large trading hubs. Where you can see the largest influence China, Korea and Japan got is in clothing style. The western style with smokings got very popular. The same goes with furniture for some reason.
If we look at religion it becomes very obvious where the reach of the land locked caravans came to and end. Islam got a very wide spread, mostly because those who practiced it where tradesmen and caravaneers. Most of the Silk routes and trade routes spaning through central Asia (and the Levant) and northern Africa are mainly populated by muslims. these places have also more often than not been hot spots for long distance travel and trade. Why they didn't reach furhter in to South-East Asia can be discussed. Mayby they couldn't get passed an established Empire like China, mayby a lot of trade was slowed down due to conflict along modern day India, Laos etc. Most like it was a mix of a lot of things.
TL;DR/ Sum-Up :
Depending on the timeframe various products have been exchanged. The most notible however, was silver and other precious metals. Quite simple China couldn't get enough of it. Later on clothing style and furniture also became a major export to the east. Today amber is a very sought out product by the Chinese, as they use it as substitute for ivory.
If you want some good books on this subjects (and other like it) I would recommend: The Human Web - A bird's-eye view of world history by McNeill and McNeill, 2003 --- Word History - An introduction by Eric Vanhaute, 2013