For a non-chemistry major, the simplest definition for pH is to say it measures the reactive ions in a solution. It allows someone to classify a solution as acidic or basic, that is, how far off of neutral (non-reactive) it is. I'm sure that went over plenty of heads, but I don't know what else to say. But other than a definition, I'll talk about how pH affects my soil.
Where I lived on the mainland, my soils were always slightly acidic, which most plants thrived in. Garden areas received a sprinkling of granular lime each spring or fall and it was sufficient to keep a happy veggie garden. I never really thought much about pH.
Things are quite different where I'm now living.....and actually trying to eke out a self reliant existence. When I started out my homestead, my soil was acidic, around 5.4 to 6. Since I live down wind from an active volcano, I get a nice dose of acid rain on a fairly regular basis. Plus I get daily light deposits of acidic volcanic ash, what housekeepers call gritty dust. On top of that, soil in my area is calcium deficient, so there is no calcium buffer for this acidity.
Besides acidic rain and ash affecting my soil, I also add various soil amendments as I attempt to make my gardens more productive. These amendments have an effect in soil pH. Composts and manures tend to acidify. Coral, shells and bone tend to do the opposite.
By the way, the amount of rainfall has an effect of pH too. Lots of rain leeches out calcium, leading toward acidic soil. Since I live in a location with normally 80" of annual rain which often comes in heavy downpours, I sometimes see a problem with leeching.
So why is pH important to me, why care? The level of the pH has a direct bearing upon which nutrients and minerals are available to the root zone -- to the soil microbes and plant roots. I could have the best combo of nutrients & minerals but they won't do any good if the can't be utilized. In soils that are overly acidic or alkaline, nutients and minerals are not available to soil organisms.
My goal is to keep my soil pH close to 6.5 to 6.8. Most vegetables like that range. I use coral sand, burnt coral chunks that have been hammered into small pieces, plus burnt bone that has been hammered into finer pieces. And wood ash. Only the wood ash adjusts pH quickly. The others work slowly, but are very important for adding much needed calcium and other minerals. I rely upon the coral and bone as my primary pH controls, with wood ash being used for quickly (meaning 2-4 weeks) needed measures. Besides, wood ash also is a good source of potassium in addition to having some calcium and other trace elements. Wood ash is a good fit for "sandy" type soils like mine.
I currently produce or gather all of my soil additives. But when I lived in NJ, I used pulverized and granular lime for addressing pH issues. Of course, they were purchased at a store. But old farmers would tell of times when seashells and oyster shells were used to help condition the soil. Some recalled their fathers crushing the shells under the wheels of a truck before spreading them in the fields. Others remember the shells being burnt first. When hiking around the back areas of NJ beside and through old farm fields, it was not uncommon to see seashell pieces sticking out of the ground. Here in Hawaii I don't see the abundant seashells that I saw on the beeches of New Jersey. Thus shells are not common enough here for me to make a special trip to gather them up for garden use. But if I see them, I'll add them to my collection bucket.