When the rails process starts, it will capture a connection to the database and hold that connection until the process stops.
For most Ruby MRI applications, you need 1 connection for each process, you will most likely run a unicorn on a hero with 3 workers on a dyno, each worker will need 1 connection to a database. When you connect to the console heroku run console, which will use the new database connection before exiting the console.
If you use a Ruby thread like jruby, then each thread will need its own database connection.
"Concurrency Ruby ActiveRecord" heroku, :