Personal training does not give you results. It gives you the best chance to get results.
I endeavor to provide the following things:
Once you sign up for training sessions, you're accountable to someone else. If you have a scheduled workout, it's on two people's schedules. You can't just skip - generally, if you just skip, you're paying for that session and getting less results and letting someone else down.
Just for that, having someone else there to train with and train for makes you externally accountable. You have a check against skipping. You have a check against failure. And you have someone else there to make you feel like you have something to live up to.
This is answering, "What now?" - what is the next thing you need to do to get your results? If your goals change, how does your training need to train?
That can be as simple as, "again, faster" or "again, heavier." But it can (and often is) more complex than that. "Again, but lighter." "This new movement instead of that." "This approach instead of that." "These movements you hate to do but need instead of that one you like but don't benefit from." Again, the best chance to succeed.
This is making sure you are doing what you intend to do in a safe, effective, and efficient manner. Expertise helps you learn to move well, load properly, and do so in the dose you need.
And that's it - personal training is giving you three tools, in the form of an external coach, that gives you the best chance to succeed. You still have to do the work, and do it with consistency, but you've multiplied your results by getting someone's help. That's the service personal trainers like myself provide.