The Irish fullback, 31, has made 292 appearances for the club since joining in 2009.
"My relationship with Seamus is so, so clear," Silva told the club's website.
"He is our captain not just because he has many years in our club – Leighton [Baines] as well – but because he has big responsibility in our dressing room.
"I think the important words about him are, he is a competitor, he wants to play every single match, he is there, and ready to help the team.
"But first of all, his mind is always on Everton Football Club.
"He is always helping his teammates, even if he is playing in his position. He is always ready to help all of them.
"In the meantime, he is fighting to achieve what he wants: his position in the XI.
"He is everything we want and what a manager wants to see in his football players. He is captain and fantastic example for everyone in our dressing room.
"First of all, it has to be Everton Football Club. After, your ambition to play.
"It is fantastic for me to have Seamus in our dressing room.
"And Leighton [Baines], he is a fantastic example as well. When you have our two captains, Seamus and Leighton, with their behaviour, all of the others are there to follow the two fantastic examples we have."