A friendship status is the state of one of your friendships, or the ability to make new friends.
The State of Your Friendships
For example, you might say that your friendship is "on the outs" with a friend you've recently fought with, and when you are unsure you'll be able to recover and become friends again. Or, if you and a long-time friend had an argument and yet you know you'll work on it because you have in the past, your status would be something like, "we're solid."
A friendship status is one that describes where you are currently with a friend. As we know, friendships can be strong for a long time with just a few bumps in the road, or they can ebb and flow and change. Most of the time, they do both.
Personal Friendship Status
Your friendship status can also apply to you personally, and your current ability to make new friends. Since people can only actively handle a certain number of friendships, their friendship status may be "full," meaning that they have so many friends they wouldn't be able to realistically spend time with that many new ones.
Or, perhaps you have one best friend that you spend a lot of time with, and as a result you prefer not to establish new friendships. You might even meet someone who wants to become close friends with you, but since you have a best friend you do things with them only when your best pal is not around. In other words, you don't encourage them in getting to know you or spending more time together. Instead, you keep them at an emotional distance.
What a Friendship Status Means
Friendship status isn't visually indicated (like the wedding ring of married people) or even emotionally acknowledged most of the time. The times that it is talked or thought about usually center around one person wanting more out of a friendship than the other person. Only then is it clear that one person's friendship status may not be in sync with their friend's.