This is caused by a component of Steam not stopping correctly, and then when you try and reopen Steam it complains.
Open a terminal window and run the following command (type it in and press enter):
ps -A | grep Steam
This will give you a list of running programs that have the word 'Steam' in them - usually 2 or 3. When I had your error and ran the above command this is what I saw:
712 ?? 700:23.42 /Applications/Steam.app/Contents/MacOS/osx32/steam -psn_0_40970
64849 ttys002 0:00.00 grep Steam
One of the items will be called 'grep Steam' - ignore that one. Each item in the list will have a number - this is the first piece of text on each line. The number we are interested in here is 712.
Run the following command to close the lingering Steam component:
Where you replace 712 with whatever number you found. If there was more than 1 number, run kill again with the other numbers too.
You should now be able to close the terminal, and run Steam just like normal. :-)