Research is a mechanic that lets you research new better tech levels for your software. If you research a tech level before AI companies, you can patent this and receive royalties when other companies use your research. Note that patenting software requires service employees with level 3 Law specialization.
It is accessible via the research icon shown below.
Research works much like the software development cycle. You need to apply the correctly educated/skilled staff to the project in order to effectively make progress.
When you are done researching a tech level, you may patent the tech level and receive royalties. Keep in mind that when an AI company researches the tech level before you patent it, the patent is instantly canceled.