The answer to your first question can be found on this Wikipedia article on Connection pool. Basically it’s a pool of connections to the DB (e.g. Postgres) being kept around and reused because opening and closing connections are costly operations.
The second question needs a more thorough analysis on your machine spec and your app’s (projected) load. I don’t think I have the knowledge to properly answer that, but my initial hypothesis is that we may set it as high as the machine’s resources let us. I might be wrong, though.
Edit: I stand corrected by Jose’s answer 
