Connection reuse

libcurl keeps a pool of old connections alive. When one transfer has completed it will keep N connections alive in a "connection pool" (sometimes also called connection cache) so that a subsequent transfer that happens to be able to reuse one of the existing connections can use it instead of creating a new one. Reusing a connection instead of creating a new one offers significant benefits in speed and required resources.
When libcurl is about to make a new connection for the purposes of doing a transfer, it will first check to see if there is an existing connection in the pool that it can reuse instead. The connection re-use check is done before any DNS or other name resolving mechanism is used, so it is purely host name based. If there is an existing live connection to the right host name, a lot of other properties (port number, protocol, etc) are also checked to see that it can be used.

Easy API pool

When you are using the easy API, or, more specifically, curl_easy_perform(), libcurl will keep the pool associated with the specific easy handle. Then reusing the same easy handle will ensure it can reuse its connection.

Multi API pool

When you are using the multi API, the connection pool is instead kept associated with the multi handle. This allows you to cleanup and re-create easy handles freely without risking losing the connection pool, and it allows the connection used by one easy handle to get reused by a separate one in a later transfer. Just reuse the multi handle!

Sharing the "connection cache"

Since libcurl 7.57.0, applications can use the share interface to have otherwise independent transfers share the same connection pool.