"Be courteous to all,
--be courteous, socially proper, get along with everyone

but intimate with few,
--be close to only a few people

and let those few be well tried
--make sure, over time, that they are worthy of your close freindship and that you can trust them.

before you give them your confidence.
--before you can trust them, or before you can tell them your secrets.

True friendship is a plant of slow growth,
--it takes a long time to grow a true friendship

and must undergo and withstand the shocks of adversity before it is entitled to the appellation."
--true friendship is built on hardship and challenges, and must go through that before it can properly be called 'true friendship.'