There are a number of chemical processes that occur when you "cure" cannabis. The main reason the smoke is less harsh is that, over time, sugars, lipids, and amino acids are oxidized and degraded. These compounds, especially amino acids, can make smoke more acidic or "acrid". The same thing occurs in tobacco when it is air cured. Also, Oxygen in the air naturally decarboxylates cannabinoid acids to some degree through a process called 'Oxidative Decarboxylation'. Aroma becomes stronger as chlorophyll breaks down and releases Phytol, an aromatic diterpene. Naturally occurring terpenes in the cannabis plant can also be converted to other terpenes via partial oxidization during air curing.
When you heat Cannabis during smoking/vaping, decarboxylation does occur but this process is not 100% efficient. This is one of the main reasons curing increases potency. Usually with a tincture, when it is properly made, it is heated for at least an hour to be forcefully decarboxylated. This converts non-psychoactive cannabinoid acids in the plant such as THCA and CBDA into THC and CBD. The heating process also forcefully causes many of the same reactions that would occur during curing to occur, such as the breakdown of Chlorophyll, and the reduction of sugars/amino acids as they react in a process known as the milliard reaction.
In my personal opinion curing isn't really necessary if you do not plan on smoking the bud or making a smokable concentrate. I use freshly harvested bud to make edibles and tinctures regularly with great results (after proper decarboxylation, of course)
https://www.ncbi.nlm.nih.gov/m/pubmed/28861498/ Decarboxylation Study of Acidic Cannabinoids
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4718604/ Medicinal Cannabis: In Vitro Validation of Vaporizers for the Smoke-Free Inhalation of Cannabis
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3296517/ Some information on the chemical processes that occur when Tobacco is air-cured
http://weather.uky.edu/aeu-93.pdf More information on the chemical processes that occur when tobacco is cured
https://en.wikipedia.org/wiki/Phytol Phytol
https://en.wikipedia.org/wiki/Oxidative_decarboxylation Oxidative Decarboxylation
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4745522/ Food Processing and Milliard Reaction Products
There is also some evidence that 8THC, a more potent form of THC forms when Cannabis is aged but I am not sure of the facts behind this. I do know that 8THC and 11THC are formed in the liver when 9THC is ingested orally. Tinctures are generally taken sublingually and will bypass the liver much like smoking or vaping, so IF it is true that curing converts 9THC to 8THC then it may result in a more potent tincture.
Cheers!