Conda is a package manager - a program where when you ask for a package to be installed, it will download an install the package you ask for and all of its depedencies (things it needs to run). The information on where to download things from and what the dependencies are for each package are stored in a database called a "channel".
bioconda is a conda channel, that contains the names, locations and dependencies of many bioinformatics tools. So when you say
conda install pysam -c bioconda the conda program will go access the bioconda channel and ask 'where do I find the package "pysam", and what else needs to be installed?' and bioconda will reply "pysam is at https://blahblah.com/bioconda/pysam/versionXY, and when you download it, copy the files to direcoty ABC and then run script fgh.py. You will first need to install the packages htslib (version > 1.2.3) and samtools (version > 4.5.6) and python (version 3.8) and zlib (verion 9.10.11)". Conda then goes away and repeats that process for htslib, samtools, python and zlib until everything is ready to install, it downloads everything and installs it.
Anaconda is both a conda channel (that is a list of packages, where they can be downloaded from, and what their dependencies are) and an installable bundle that includes python, the most common data science packages for python (including things like scipy, numpy, pandas and matplotlib) and the conda pacakge manager.
miniconda is a different bundle that you can download from the same place as Anaconda, and it includes python and the conda package manager, but not the common data science packages, which you would have to install manually using the conda package manager if you later decided you wanted them.