github allows two different methods to access your repository: https and ssh.
In the first version of your question, you configured git to access github via ssh. Therefore git calls ssh which tries to read your keys and asks you for the passphrase of the ssh-key.
When you create your ssh key, you may protect it by a passphrase or decide not to do so.
In case you decide for a passphrase then you either have to type the passphrase each time you want to use your key (i.e. push, fetch, etc.) or you can use ssh-agent. In the last case you only have to type the passphrase once when adding you key to the agent. Afterwards the agent will do all authorization for you.
On Windows you can use the PuTTY tools to manage your keys:
http://www.chiark.greenend.org.uk/~sgtatham/putty/download.html
You can use puttygen
to generate a new key or change an existing one. (for example to remove the passphrase)
You can use pagent
as a ssh agent. After starting it will reside in the notification area. Click on the icon to add your key.
Once your agent knows about the key, you should no longer be asked for your ssh passphrase.