[Oh Ya1]

I got a Lumia 620 for my parents, who don't understand technology AT ALL. Is it possible for me to remote install apps for them?

[o0Nighthawk0o]

You should be able to log in to the phone store with their account. Have them make sure they have a WiFi or data connection. Find whatever app and click the install button. This should push install the app to the phone.

[DBDev]

You can do that from www.windowsphone.com

[Sekyal]

Probably will have to have them setup phone first to allow remote install. I know I had to do that. Turn on "Find Phone" in settings. It may show it is off when it is really on, kinda bizarre.
Also there is a Windows Phone app for the store on Windows 8 called Windows Phone Store. It isn't official but it works quite well.

[neo158]

I got a Lumia 620 for my parents, who don't understand technology AT ALL. Is it possible for me to remote install apps for them?

My father isn't that good with technology but as soon as I got him using Windows Phone he found it so much easier to use than his Android phone, as others have said remote install of apps is possible through the methods they mentioned.