It's great.
You have no idea who will walk through the door next and what they will ask you to construct, hence there is an element of surprise.
It could be the most ill-conceived idea in history, or it could be Alan Turing, accompanied by Lady Ada Lovelace, and they have no idea what to do with two new inventions they have just made: theoretical computer science and a computer.
Your next project can be anything -- from figuring out that a client's computer is not turning on due to plugging the power strip into itself to building an AGI.
Who cares if it is theoretically impossible!
The client will say that, so at the very least, you have to know better, then tell them diplomatically.
In short, the skill set is a true jack-of-all-trades.
But, since every college-trained monkey is convinced s/he has what it takes to do what you do, there is always competition, with the client will say, "why should I pay you $200/hr when I can pay the soon to be college-trained monkey $2/hr?"
Have fun explaining the price difference to a non-technical client!!! That's why we charge $55-$75 per hour, not $200 per hour.
As to the actual work:
If the system is too buggy to be delivered and used, you lose payment for the entire project, and you will have someone telling all their friends that you suck. Don't hire you! One unhappy client is equal to 10 happy clients in the effect on your marketing!
In short, I LOVE IT, as it is never easy ... thus, I will never be bored. I feel sorry for you 9-5 stiffs, working on the same boring project, day in and day out!
But, then again, I am on duty 24/7/365, because due to the first law of software engineering, who knows when some life-critical system that we maintain will have a bug.
So, freelancing really is not for the faint of heart.
Disclaimer: About 2 months ago, I first used the term rent-a-CTO to inject a little humor into my Quora bio. I never thought it would become an actual title or that others on Quora would ask me how to become a rent-a-CTO. I guess part of being a rent-a-CTO is knowing something about marketing.
Now, for the actual answer................
The best way to explain a rent-a-CTO's function is to describe a typical first meeting between a rent-a-CTO and a prospective client.
Client: I have a fantastic idea to create the next killer App for Super Bam Bam ... It's based on the widgetized blunt instrument tech deployed by hyper-speed, framed https://en.wikipedia.org/wiki/CGI.
Rent-a-CTO: Let me see if I can translate this into English: You want to make a replacement for Bam Bam's club -- the one he used to hit Dino over the head?
Client: Yes but it is so much more! We can use it to gain hyperdimensional market share in the infant learning tool market!
Rent-a-CTO: Even for fictional, superhuman, Stone Age-era babies, the toy market is pretty large. You might want to focus on club replacements for now. By adding too many features early on in the process, you will complicate delivery-time estimates, possibly causing product liability issues, particularly if you try to market to real babies, as opposed to their fictional counterparts. So lets start there, O.K.?
Client: That sounds good. I guess I was over complicating things. Do you have any ideas that would increase the impact power of the club by 200%?
Rent-a-CTO: Well, that goal might be a little unrealistic, but in beta, I think 50% with a second-version goal of 100% is doable. From what I know of the Stone Age-era club market, this should be enough of a competitive advantage that any modern Stone Age family will sell their first born for it.
Client: How much time should we budget for?
Rent-a-CTO: Give me a few days to do some planning, and I will get back to you. What are your sales projections like? Do you have any technical skills, or do I need to build a day-to-day team?
......................and so forth.
A rent-a-CTO can take an idea from inception to completion.
If a team is in trouble, and needs to be turned around in a hurry, we can also step in to save the day. In short, our job is to get your company on the right technical track without saddling it with the financial burden of a full-time CTO.
As my client Jimmy Flores mentioned in his answer, the relationship can be short-term or long-term; the rent-a-CTO/client relationship takes many forms. The main idea is that startups rarely need a full-time CTO.