Git alias:

bsd = "!f(){ \
    branch=\"${1:-$(git rev-parse --abbrev-ref HEAD 2>/dev/null)}\";  \
    git config \"branch.$branch.description\"; \
};f"

Example:

git bsd
This is an example branch

We advocate for git authors to add this feature in the future as git --show-description

Compare git bed in order to edit the branch description.