it's arbitrary and based on the number of posts you have made, you can change that in your Settings, use a custom message if you like.
Oh, I thought you had to be a grumpy old man (remember, women are never Senior; they are just Mature). I got the "old man" part correct, but I need more work on the "grumpy" part.
The term 'Senior Member' is reserved for those who post nonsense for the sole purpose of raising their post count.