Complete means done. Completely. It means you can send the version you believe is already publishable, right now.
If you are still fiddling with the content, it isn't done.
Publishers do not care if you have had readers, alpha or beta, because they don't trust your readers (no offense). They don't care how many revisions you did, none or a hundred, they only want to see your final product. You will get no sympathy or consideration whatsoever on how much work you put into it.
They trust agents that are professional readers. They trust their own hired readers that are professionals, and can analyze your story.
The reason they trust agents is because the agents filter out 95% of their submissions and only present them with well written stories.
To do that, agents ask for the first "N" pages of your manuscript, maybe 3, maybe 10, and from that they can tell if you know how to write a story.
Many agents surveyed say they will toss a story in the reject pile before they finish the first page, sometimes before they finish the first paragraph. One agent said if she (most are women) sees a query that says "I have written a fiction novel", that's it, it is rejected.
They have to, they can only represent a limited number of books at a time, and they may get 20 or 50 times as many queries as they can possibly work. Even then, if your sample passes muster, then they will ask for the whole work, and make a judgment on that.
That is one of the main reasons being a literary agent is even a job; this screening is a very valuable service to publishers. Agents bring them only exactly the kinds of books they want to publish, and only good material to consider.
Many (not all) publishers will work exclusively with agents, that already understand publishing lingo, slang and concerns. And will stop using an agent if they persist in pitching books that aren't what they have made clear they are looking for.
This is a grinder to get through, but first-time writers do get through it to paid publication every year.
Personally, I hired a retired literary agent to critique and review my pitch letter, my sample pages, and my synopsis, until they were up to snuff.