For an email, to 'sign in', you put in your email address, and your password, and then you click the sign in, or Log in, button. Another way to say sign in, is Log in. The opposite of Sign in/Log in, is Sign Out/Log Out.
"Signing in to my email"
"I am typing in my email and password and then going to press a button"
"Cool, can I 'sign in' after you?!"