Kevin Hill explains the minimum and maximum server memory options in SQL Server:
Min Server Memory seems to get the most bad information spread around. SQL Server does NOT automatically grab memory up to the Min setting when it starts. However, once it gets there, it doesn’t give back.
Back to the car analogy…if you start up and head off down the road at 20 mph, you are above the default (0), but not at the max (100+, depending on the car and the tires…). If you set the cruise control, you can accelerate up and down above 20, but you won’t go below that unless you hit the brakes.
I do like the car analogy to his post.