Software is real - both as a product (economic, social, cultural value) and as a concept (utility, user interface). The processes and systems invented to develop both software and hardware are also real (as opposed to only hypothetical and theoretical) - they are real in the sense that they exist, actually, and can be utilised to achieve whatever outcomes originally conceived by the inventor/developer, e.g. developed to solve a problem or address a practical need.
Some software is developed to allow users to interface with hardware. For example, using a keyboard to interface with hardware (hard-disk, CPU, monitor) in order to send instructions to a word processor application. Or, to use software developed to allow users to input text into a website's search field - and then for the website to run your request on a web server, and return a useful result - whether a query about news or a maths calculation.
Some software, such as that developed for CPU temperature measurements, don't require any direct input from the user. But, still - in order for the hardware to perform efficiently, the hardware must be instructed by the logical processes embedded within the software.
During the NASA Apollo missions, the software was embedded not (just) within virtual interfaces, but also hardware-based devices, with real switches and knobs - used to instruct the hardware (command and service module) what to do and when.
Ultimately, all software allows us to control hardware through an user-interface, and then allowing for further reactions to the results (output) of our interfacing via the software. All software is an encapsulation of our intention, expressed through formal logical structures, necessary for effective manipulation and utilisation of hardware.
Ultimately, all hardware is a spontaneous reaction to and the organisation of electricity and electrical signals.
Like art - software and hardware exist, actually, by virtue of the fact we conceived of them, but our dependency upon software is arguably much greater, and so, by now, software... has much greater value to our tech-oriented society.
Like most things conceived by humanity - the ultimate intention and purpose is to control and harness the fundamental laws of nature in order to guarantee survival.
Some software could be considered trivial, and some - such as those controlling essential life-support hardware, are held in the highest possible regard (value).