They're configuration files for different *nix programs. For example .vimrc for vim. Or .bashrc for bash. In those dotfiles you can customize how things look or add custom commands etc.

This post is about how you can automated some of that so you can easily replicate the environment you're used to everywhere.

In this context, it's referring to various configuration and settings files, which traditionally on Unix platforms are saved in your home directory, either directly as hidden files or within hidden directories (for when there are multiple files needed).

Some examples would include .bashrc for running commands automatically when bash starts, .vimrc for vim preferences, .ssh/ for storing SSH keys and settings, etc.