Supply drops are essentially crates that "drop" (spawn in every 10 minutes) and give the first player that finds it and "opens" it 3 random items, along with 10 Gems per supply drop. If a Mythic-tier item is collected in a drop, an automated message will appear in the in-game chat which reads "<USERNAME> got a/an <ITEMNAME> from a Supply Drop!".
Every 10 minutes, a supply crate spawns in the map. Players will often race to be the first to open it. The first player to touch it (in essence, open it) will receive 3 items, plus 10 Gems. The location of the crate is marked with orange text saying "SUPPLY DROP" in all capital letters. It can be seen from far away.
The crates used to sometimes be irretrievable as they could have spawned in areas like the inside of a rock. When the newer maps were released, this was fixed.
Usually, the rarities of dropped items range from Common to Mythic - thus including Omega-tier, Exclusive-tier, and Mythic-tier items. Mythic-tier items tend to be more commonly found in supply drops than Exclusive-tier items, due to the number of items in each tier.
Past items (that used to be available in Supply Drops) include Darth Vader, Grandma, and Golden Apple. As soon as an item becomes Exclusive-tier, it is no longer available in supply drops (unless a special exception is made by Sam, either because of an event, or on a case-by-case basis such as with Grandma and Darth Vader).