Q:

What happens when I block someone on Steam?

I'm 'away' for a week and would like some friends not to know I'm playing games. What does blocking a friend actually do?
I'm just looking for it to show me as offline and not show what game I'm playing or if I'm online or not.

A:

To specifically answer your question at hand, blocking someone will make it so you appear offline to them. No notifications are sent regarding your status or game-playing. They WILL still be on your friends list (and you'll be on their list), so you have easy access to unblock them at any time. Blocked players who are unfriended are still blocked, and they cannot send you another friend request.
I have personally used 'blocking' to temporarily set myself as offline to a specific individual or small group of people while being online to everyone else. I have also personally verified this through my wife's steam account too.
Just keep in mind your steamcommunity profile is public, so if anyone happens to visit your browser profile (e.g. steamcommunity.com/id/yourprofileid) while playing a game , it will say you're in-game. I don't think that will really be a problem, as I'm assuming there's not really a reason for the people you're blocking to visit your browser profile. Setting your status to 'Appear Offline' DOES make you offline across the board, including steamcommunity.com.
Additional note: The other answers here spurred me to do some additional testing with this. If the person you're blocking is online when you block them. You will permanently be 'Online' to them until they close or restart Steam. If you want to covertly block someone, do so while they're offline so when they log in next you will appear offline to them.
If you're not patient enough to wait for someone to go offline, you can do the following:

In your friends list, click the dropdown of the player you want to block and select 'Send message'
A chat window pops up between you and the other player.
Back in your friends list, click the dropdown next to your profile and go offline. When you do your entire friends list is replaced by a sign in button.
Go back to the chat window you opened with this player. Click the dropdown next to their name and click 'Block all communication', then block them.

This effectively allows you to block players while you appear to be offline.

A:

I tested this a few months ago and unless it has been patched what you have written is incorrect.
I blocked my friend whilst on skype with him. He could see I was online and he could open up the instant message box and appear to send me messages but I didn't get them and he got 
no indication they were not sent.

