Best way to present my work to new clients?

Hi everyone,
I've seen posts here mentioning showing people your "book". Is it like just an album of your work or are there extra things to make it stand out? Right now I have an Instagram page and a Facebook page that have all my photos. I usually just show people these photos when they ask about my work. I like the idea of an album or portfolio that I can take to meet clients, as it feels more professional to have something they can flip through and view instead of whipping out my phone.

I'll be honest I've never been and met a client like that, I just refer people to my website or sometimes will show people my website on a tablet. That would probably be more professional and 'modern' than a phone or a book?