This is a work in progress
Hemoglobin in your blood carries oxygen. The percentage saturation of the hemoglobin is a measure of health. For example, a patient with pneumonia may be monitored for oxygen saturation. Oxygen may be administered if the saturation falls too low.
I worked for Nellcor at one time, the original developers of the pulse oximiter. I helped validate the algorithms in the N-20, their first portable device. Devices have gotten much smaller since then (1992). About 15 years ago REI sold the SportStat, a miniaturized pulse oximiter for about $400. I have taken that device on almost all my hikes. Nowadays, you can get one online for $20-$30. Walmart sells one for under $40.
Oxygen saturation decreases when going to higher elevations. There is less oxygen in the air for the hemoglobin to grab. The most interesting observation I have made is that a few days after entering high altitude my oxygen saturation increases by a few percent. Here is quantifiable evidence that hikers can acclimatize by spending days at high elevations prior to a hike.
The plot shows my O2 saturation for one hike to the Kaweah Basin in 2015. At the bottom I have labeled the sample from the first campsite. The samples go clockwise; my saturation initially decreasing as my altitude increases. Once at about 11,000 feet, the saturation slowly increases by a few percent over the next few days. It continues to be higher through the final camp nine.
The body detects the presence of CO2 and uses it to determining how much to breathe. Breathing faster at high altitudes blows off your CO2 but doesn't quite bring in enough O2 . It does raise the blood pH though. The body catches up a few days later by excreting bicarbonate, which lowers the pH and allows more CO2 to dissolve, which signals you to breath more.
A follow-up question might be: Why? What benefit, evolutionary-wise, does it have to develop a temporary system for increasing your oxygen saturation? Perhaps for pneumonia. The extra little benefit might be just enough for survival when congested lungs prevent full oxygenation of your blood.