When setting up connections to sites, curl keeps old connections around for a while so that if the next transfer is done using the same host as a previous transfer, it can reuse the same connection again and thus save a lot of time. We call this persistent connections. curl will always try to keep connections alive and reuse existing connections as far as it can.
Connections are kept in the connection pool, sometimes also called the connection cache.
The curl command-line tool can, however, only keep connections alive for as long as it runs, so as soon as it exits back to your command line it has to close down all currently open connections (and also free and clean up all the other caches it uses to decrease time of subsequent operations). We call the pool of alive connections the "connection cache".
If you want to perform N transfers or operations against the same host or same base URL, you could gain a lot of speed by trying to do them in as few curl command lines as possible instead of repeatedly invoking curl with one URL at a time.