What is Arnica?
In short, arnica (Arnica montana, along with a few other species) is a plant with a reputation for healing in traditional medicines.
A quick literature search shows that the science behind the use of Arnica to treat inflammation is largely lacking (source), but there is some support for how it might work in vitro, through a compound it contains called helenalin.
However, at least one abstract I came across indicated that topical arnica treatment does not alleviate pain (source).
It's important to note the tiny size of this study, and I found it interesting that while most of the articles I came across did not report significant findings suggesting the medical use of arnica, they all called for further investigation (seemingly based on the promise from traditional medicine, and hints at molecular mechanism from the in vitro studies connecting helenalin to NF-KB).