What do ants mean?

I do some yard work for my neighbors and notice they have a lot of ants in their yards. One neighbor has flower beds where there are ton of red biting ants. He sprays ant killer on them to be rid of them, but that doesn't seem to do anything. In another clients yard I no longer work at they are in flower beds. The ground was covered in oak leaves and the soil arguably in good condition high in organic matter. They were paying me to remove the leaves as well as weeds and tree sapplings.  

Is there a use for ants in a permaculture mind set or a reason they appear? I understand from the Rodales guide to Composting ants add magnesium and phosphorus to the soil. It seems their nests would additionally allow the passage of air particles into the ground aka aeration into the soil. I've noticed atleast 3 nests nestled up on the plant stalks. My one client believes it will eventually kill the plant so he sprays the nests and destroys them off his plants. I'd appreciate any thoughts on this.

As a general rule -- and this post is a good example -- you'll get much better information if you include your location, either in your profile (which will show on the page) or in the relevant post.

Ants vary tremendously. I don't think of them as reflecting much about the garden except the presence of a food source somewhere nearby. I know snakes and lizards like them, and I like snakes and lizards, so I see them as a positive in my situation. Unless they're encouraging aphids on my food plants. Aphids I squish. The ants, meh. But these aren't biting ants.

Actually, that could be a good point about location. When I think of ants I think of fire ants. When I see a fire ant mound I assume there's a source of water nearby. But I also expect the soil to be pretty barren where they are. They like bare soil and sparse vegetation. Maybe they don't encourage this by feeding on the soil life that builds soil fertility, but the only improvement I've seen in soil with fire ants is after they've been driven out. In fact, the only nontoxic methods I've seen work for fire ants involves increasing soil life.

https://permies.com/t/37050/role-ants This thread talks about this topic and some people there have seen benefit to ants. There's even someone there who thinks you can find the fire ant mounds by looking for the health grass, which is amazing to me.

Even better, when I used google I was able to find this thread https://permies.com/t/13415/critters/fireants-pants where a couple of people explain how they've managed to use the fire ants to obtain planting soil and to dig holes for planting trees. I remembered the tree planting in particular because it made me laugh out loud in a doctor's office when I saw that someone had managed to make fire ants productive.

I don't think ants mean much, other than the fact that there are just a whole lot of ants in the world. Both ants and beetles outnumber humans by sheer body weight. Crazy, huh?

Ants are a great food source for many kinds of birds that also eat other insects, including the kinds of insects that eat your vegetables. So a big ant population might attract insectivores to your yard. Plus, many ant species' favorite food is honeydew, produced by aphids and some other pest insects. These ant species actually corral and tend honeydew-producing insects, keeping them in specific areas near their nests. So if you have a lot of aphids, maybe you could plant a few sacrificial tomatoes or nasturtiums near the ant nest and see if the ants start moving aphids out of your garden and closer to their nest, where they won't do any damage to your crops.

Ants are generally helpful and useful critters, but they can definitely be annoying in the home. We've got odorous house ants just starting to come into our house right now. Ugh. We are using bait to get rid of this nest, but I don't bait or spray ants outside. They don't bother me out there, even when they crawl on me.

I came across this post because my tomatoe raised beds are full of ants and was wondering if that was bad or just a leave it be situation.

As far as ants in the house we had a few once, and i was told they were scouts and to wash their hormone scent away with vinegar and it totally worked! The ants never came as a highway!!

I've also heard the won't cross coffee grounds

For ants, use coffee grounds.

 spent coffee grounds, you need to cover the mound and all around at least 1 meter from the outer edge of the mound.  make the grounds a 3 cm thick layer

From this thread and see other suggestions:  https://permies.com/t/73451/critters/Ant-infestation#611937