The
eval `ssh-agent -s`
sets the environment of the process. If you are using a window manager e.g. on a linux machine then the window manager will likely have a possibility to run a program like e.g. your ssh-agent on startup and passing the environment down to all processes started there, so all your terminal windows/tabs will allow you a passwordless login. The exact location, configuration and behaviour depends on the desktop/wm used.
If you are on a non-window-system, then you might look at the output of the ssh-agent call and paste that into all shells you open, however that may be as complicated as entering your password. The output will likely set something like
SSH_AGENT_PID=4041
SSH_AUTH_SOCK=/tmp/ssh-WZANnlaFiaBt/agent.3966
and you can access pw-less in all places where you set these