The Fancy Solution: (Hard, Not Free, Fancy)

Setup a website for you own and ask the developer (or find some plugin if you're planing to use wordpress (most likely)) to add an option to your website to give the possibility to the client to watch/download only his/her photos from your cloud solution by that specific username/password combination that you provide to them. By this way you can always have a backup from all of the images that you have given to you clients in one place (in case they needed it again) and if they gave the permission to you to share the images you'll be able to add them to your portfolio section of your website easily without hassling about uploading them again to somewhere.

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The Good Solution: (Easy, Free, Secure (Password Protection))

Mediafire is probably the best solution if you want it to be free, easy, secure and kinda fancy. With the free account you'll have 15GB of space, which you can even create an folder on your computer and setup mediafire's Windows/Mac client (not necessary) to auto-upload the content. you'll be able to protect your files by passwords. The only downside of the Mediafire is that it has some ads on the file download page which will not be a big of a problem but it makes it a little bit infancy solution if you're working with some serious clients.

Alternative: MEGA (Easy, Free, Secure, 50GB Space, Ad-Free, Auto-Sync, But Needs App)

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The Easy Solution: (Easy, Free, Needs App)

You could use Facebook (messenger) to send their photos at the full size, and almost everyone has/uses facebook these days, it's free, easy to upload but your client will need facebook messanger and it's infancy and not-so-centralized.

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The Efficient Solution: (Easy, Free, Registration Needed)

You could use Telegram messaging app if you just want to deliver photos to the client in an efficient (but not so fancy) way, on Telegram you can send huge files (Up to 2GB per file), it's free, it has secure chat option with message auto-delete feature and it's also available iOS devices, but if your client doesn't have Telegram already it's gonna make the situation ugly a little bit.