In a nutshell, Mamba is simply a recoding of Conda in C++ for massive performance gains.
It features several design choices that speed up the process of creating environments or installing packages such as:
You can learn more by reading Mamba's GitHub: https://github.com/mamba-org/mamba or the full documentation: https://mamba.readthedocs.io/en/latest/index.html
In addition to much faster installation times, mamba utilizes the same command line parser, package installation and deinstallation code, and transaction verification routines as Conda to maximize compatibility.
In other words, Mamba is just faster Conda with some cool added utilities and improvements.
The primary motivation for creating Mamba was to solve the two major performance issues of conda, namely speed and memory usage.