Apple made a few big announcements Monday, marking a strong push into cloud computing and taking on a lot of new competitors along the way.

The big announcement of the day was iTunes in the Cloud, one of nine applications that are a part of the company’s free — yes, you read that right — iCloud suite of apps.

What is iCloud?Nine apps make up iCloud: calendar, contacts, apps, App Store, iBooks, backup, documents, photos and iTunes in the cloud. Users get 5 GB of storage for free — purchased songs, apps, photos and iBooks don’t count against your free storage.

Doesn’t Apple already have that? Apple has a service called MobileMe, which has calendar, documents and e-mail in the cloud, for $99 a year. Apple founder Steve Jobs said MobileMe — largely acknowledged as a failure — will be folded into iCloud.

What is iTunes in the Cloud? With iTunes in the Cloud, users can sync any files they bought in the iTunes store across devices and it requires no upload to do so. While the service isn’t a streaming music locker like Amazon and Google’s forays into online music, it does give Apple customers greater access to their libraries from anywhere.

What does it cost? iCloud is free for 5GB of storage, but if you want to add music that you didn’t buy on iTunes, then you should be interested in Jobs’ “one more thing” announcement.

He also introduced iTunes Match, a $24.95-per-year service that will match any tracks in your cloud library that you didn’t buy from the iTunes store. (That includes those songs you’ve probably been stealing all these years through bit torrents and file-sharing services.)

What devices can use it? Any device with iTunes can use iTunes in the Cloud, so your Mac and PC, as well as your iPhone, iPod Touch and iPad. You can’t use iTunes in the Cloud on a device without iTunes, so that means no service for Android devices, BlackBerrys, etc.

How does it compare to Google and Amazon’s music services?

There are a few key differences among the music services. With Apple, your music can’t go anywhere you have an Internet browser — a disadvantage — but it will be the same on your tablet, phone and computer. That eliminates a lot of the annoying aspects of a multi-gadget life.

But with Google and Amazon, users have to spend the time to upload their entire libraries, but Apple will do it for you for any track bought through the iTunes store (as well as those you didn’t, with iTunes Match.)

Jobs also makes the argument that iTunes in the Cloud is cheaper, since Amazon charges $50 per year for 50 GB and $100 for 100 GB of storage. Apple lets you store and match up to 20,000 songs for $24.95. Google offers 5GB — about 2,000 songs — for free through its beta program, but hasn’t announced official pricing.

Did Apple announce anything else? Updates to Apple’s operating systems — mobile and PC — were a bit overshadowed, but there are a few exciting things to share.

For one, the next version of Apple’s OS X, Lion, will be $29.99 and the 4GB download will only be available through the Mac App Store. Lion integrates more of the mobile aesthetic into the desktop operating system.

Apple is also going after BlackBerry and its Messenger service with iMessage, an Apple-only messaging system for iOS 5. And starting with this operating system, updates will be over the air, meaning you won’t have to go hunting for a USB or FireWire cord every time Apple rolls out another update.

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