  Considerable observational efforts are being dedicated to measuring the
sky-averaged (global) 21-cm signal of neutral hydrogen from Cosmic Dawn and the
Epoch of Reionization. Deriving observational constraints on the astrophysics
of this era requires modeling tools that can quickly and accurately generate
theoretical signals across the wide astrophysical parameter space. For this
purpose artificial neural networks were used to create the only two existing
global signal emulators, 21cmGEM and globalemu. In this paper we introduce
21cmVAE, a neural network-based global signal emulator, trained on the same
dataset of ~30,000 global signals as the other two emulators, but with a more
direct prediction algorithm that prioritizes accuracy and simplicity. Using
neural networks, we compute derivatives of the signals with respect to the
astrophysical parameters and establish the most important astrophysical
processes that drive the global 21-cm signal at different epochs. 21cmVAE has a
relative rms error of only 0.34 - equivalently 0.54 mK - on average, which is a
significant improvement compared to the existing emulators, and a run time of
0.04 seconds per parameter set. The emulator, the code, and the processed
datasets are publicly available at https://github.com/christianhbye/21cmVAE and
through https://zenodo.org/record/5904939.
