It's been a while since I've dealt with a client and hotmail. A while back hotmail was only accessible via the web interface.... you then had capability sometime later of accessing it via an email client. Which Hotmail got rid of a time later... well they forced you to pay a subscription to access the account from a mail client such as Outlook.
It's obvious that Hotmail turned this around with the rising of GMail and other free email services that allow you to access the email via the web, and from devices. Hotmail was accessible again via a pop service. But now there is much better interoperability with hotmail and computers/devices. With the changeover to Outlook.com you can connect to Hotmail with a much nicer syncronising type
Outlook accounts allow you to syncronise your emails, calendars and contacts with the web which make this a very cloud like service, much like an Exchange account. This is great for a free service!
So let's add an account to an iOS device. Go to Settings, then Mail, Contacts, Calendars. Hit "Add Account". Choose an "Outlook.com" type account. You only need your email and password and that's it. Choose which items you want to syncronise. This can be Mail, Calendar and Contacts.
Adding to your Mac Mail is just as easy. Go to "Mail", "Preferences", "Accounts" and add a new account. Enter just your email address and password and it will automatically detect the settings you need. Again, choose the items you want to syncronise.