Photometric is a descriptor for measurements involved in photometry. When you’re dealing with light, you’ll either be looking at photometric or radiometric (see below) measurements.
There are two different measurements because the way people see light is a lot different than how machines see light. Our brains weight colors differently. The same amount of light from different wavelengths can look like they have totally different brightness. Our eyeballs love the color green so compared to red light, we make green light look brighter. To get a red light and green light on a Christmas tree to look the same brightness to our eyeballs, we have to crank the red light up.
To account for how our eyeballs change things, we change measurement machines to work the same way as our eyeballs. When we do that, we’re going from radiometric measurements to photometric measurements.
Put another way: if the red and green Christmas lights looked the same to photometric equipment (and our eyeballs), the radiometric equipment would tell you the red light was much brighter than the green.
All the unit names for photometric measurements get changed, too. When you’re dealing with photometry, the most common units you’ll use are luminous flux measured in lumens, and luminous intensity measured in candela.
So, if you’re working on something where it matters how a human eye is going to see it, you want to make sure you’re working in photometric units.