Time to market

Time to market of features or increments means how long does it take for a feature to be requested until it is available to the market user. I don't know what commerical time to market means, but my best guess would be it is the same thing?

Is time to market only relate to agile? Or this is an independent conception that can use in standard business without agile?

T2M is not a concept specifically stated in Agile. But as said, one of the things agile focusses on is the process how to deliver value to this market (and how to avoid Waste, where Waste is also time wasted) so it is a "natural" part of Agile

Time to market is still a thing in agile but it changes slightly.  Old days of waterfall, time to market was how long the project would take to complete (including any of the extra time put on because almost all waterfall projects needed it.)  In agile, time to market is still a term but how you define the deliverable changes.  Since in an agile environment you wil be incrementally delivering value and adjusting based on feedback given from the previous increment you have to have some way of determining you are completely done and what is it that is done.  in agile, you continuously deliver so the time to market is basically the timebox you use between deliveries and inspection.  In a Continuous Integration/Continuous Delivery (CI/CD) world you could have a time to market of hours.  

Time to market is still a metric in agile but in my experience it becomes less important in agile environments.

Look at the Time to Market with a supply chain perspective. In a traditional commercial business setting, the time to market refers to the delivery of the product in its entirety as it is intended to be used by the customer.

In an agile setting, where the scope is not well defined, the value delivery is incremental and the customers may and do influence the delivery of the remaining increments. You may have delivered "some" value incrementally but may not have delivered the value "as intended" by the user/customer. For this reason, every increment or time box cannot be treated in the same manner as it is treated in the traditional commercial setting.

Hence, the Time to Market concept in agile is tweaked to reflect the time that it provides value by either through internal use or generating income.