The Last Account Activity Feature is handy because it allows you to see when and where your account has been accessed. It may be previous sessions on the same computer or sessions on a different device. You can see when I accessed my Google account through mail on my iPad in the log of activity.
If there was activity from a a city or location where you have not been it may be a sign someone is hacking in to your account. Besides being helpful and letting me know if I should consider changing password, it gives the option of signing out of all other sessions remotely. So, if I forget to sign out somewhere, I can log in from another location and sign out of all other sessions! Very handy stuff because, hey, this can happen to all of us. Also, very handy for students to know so they can help keep their accounts secure. Students forget all the time, showing them this feature is another way to teach them about keeping their Gmail account safe.
You can read more about Google's Last Account Activity Feature here.