Process is a concrete instance of that effervescent multiplier in a startup: execution. It certainly is not execution itself, but is a repeatable (and repeating) building block of a current execution strategy -- especially in a particular aspect of the business (sales, dev, market validation, etc). It is the day-in and day-out patterns of behavior that your team makes into habit until they are virtually invisible.
A lot of teams think that you heavy process is bad and os they aim to be 'lightweight' saying things like 'we don't want to come up with a process to slow us down, let's just do stuff'. This is half right. A heavy process is unnecessary and distracting early on and most processes you make up beforehand are going to suck for your actual workflow, becoming a perfect example of premature optimization.
That being said, there isn't any such thing as 'no process'. Regardless of whether you say it or not, you're going to fall into a routine that will end up being your process. This is a relief to know at the beginning. You just start off with your Minimum Viable Process and don't have to get bogged down planning one out. (I think it is this process planning more than the process itself that gives process a bad name in really early stage teams). However, like your product, sales and every other aspect of your business, you need to iterate on that process to improvement. This is where thinking 'we have no process' is dangerous. How can you self reflect and improve something you don't acknowledge is there?
It is helpful to reflect and discuss your processes with your team every so often to figure out what is working, what is not working and how to move forward.