You're correct that an antibiotic will kill (anti-) something that is alive (-biotic), specifically, bacteria. The formal definition of an antibiotic is a substance that will either inhibit the growth or replication of a bacterium (singular) or kill it. This is different from an antimicrobial substance.
Now, exactly which bacteria an antibiotic will kill (some of them? all of them?) depends on the type of antibiotic. For example, some antibiotics are highly specialized to target specific types or species of bacteria. But there are also broad-spectrum antibiotics that target a wide range of bacteria.
As an analogy for using a broad-spectrum antibiotic, imagine you want to get rid of a couple of types of weeds in a yard. If you spray broad-spectrum, sure, you'll likely kill the weeds. But you may also kill the grass, the nearby clover, the mushroom filaments underground... all kinds of organisms. In this analogy, the yard is the human body and the plants and fungus are bacteria.
So if you take a broad-spectrum antibiotic, could it kill all bacteria in a body?
Perhaps, but such a powerful antibiotic would be seldom used. Why?
Since there are more bacteria cells in and on our bodies relative to our own cells, there is a huge amount of bacteria that are beneficial to us. Our health may be drastically affected if we were to kill too many of our bacteria. It may help to imagine the human body as a vast community of billions of cells that are living and working together to survive and reproduce.
There's a dangerous consequence of overusing antibiotics, especially powerful ones such as vancomycin (think "vanquish"). Let's revisit the yard analogy:
Suppose a person takes a strong broad-spectrum antibiotic.
It kills a large amount of bacteria. This opens niches in the body for other bacteria to colonize and grow:
"Where did everyone go? There used to be a lot of bacteria living here."
"Looks like they were wiped out."
"Great, let's move in!"
"What's wrong with your bacterium friend over there?"
"Oh, he got beat down by that antibiotic, but he's getting better."
"So he's resistant to it?"
"Yep, lucky for him."
What's the issue with leaving a small proportion of bacteria behind which are resistant to the powerful antibiotic? We have artificially selected for the resistant bacteria--and we've opened up new territory for them to grow. The overusage of antibiotics, especially at the community level, leads to the selection of superbugs that are highly resistant to antibiotics: they're hard to kill.
This is also a consequence of the over-use of antibacterial gels, which are primarily alcohol. If we continue killing the majority of weak bacteria on our hands, we are artificially selecting for more resistant bacteria.
As an example, look up the bug MRSA: methicillin-resistant Staphylococcus aureus.