1. even more; still more; all the more; more than ever
彼はそれまでよりも一層小さな声で、そう続けた。He continued in a voice even smaller than before.
2. one layer
このガラスは一層ではなく二層になっている。This glass isn't a single layer; it has two layers.
3. lowest floor (of a building)
4. rather; sooner; preferably