Sounds like a standard, run-of-the mill "dive and drive" style non-precision instrument approach. With the advent of commonplace GPS based approaches, they have become less common than they used to be, but they still exist and are safe to use.
Non-Precision means that you are using a simple ground-based navigation aid that does not provide vertical guidance, (a glide path indication) for example an NDB (Non-directional beacon) or VOR (VHF Omnidirectional Range) So, there are intermediate "step-down" fixes, that require you to maintain a certain minimum altitude until you reach a certain distance from the navaid. The route and altitude requirements (obstacle and terrain clearance) are selected by a well documented process called TERPS / FAA Order 8260.3F. (Edit, oops up to F now.)
There's always been debate among pilots about whether these approaches should be flow using a "Continuous Descent" method, where you select a descent rate to try to arrive at the altitude crossing restriction exactly before the next one comes into effect, or if you should descend rapidly to the altitude restriction, then level off until the next altitude restriction arrives, AKA "Dive and Drive."
There are pros and cons to each method and you can find well respected flight instructors that advocate for each. But a "Dive and Drive" approach can put you visually close to the ground when you are still pretty far from he airport. Really, modern GPS based RNAV approaches make the whole debate close to obsolete. Any podunk airport can get a satellite based precision approach with no significant investment in equipment, just a survey and some lighting improvements.