The bronze medal shown was an official commemorative piece issued jointly by the 1984 Los Angeles Olympics Organizing Committee and the 1984 Sarajevo Winter Olympics Organizing Committee. It was to celebrate international unity and "spirit of peace" via the Olympic Games.
Note: The medal is reported to be the first medal jointly sponsored by two Olympic Organizing Committees. I'm not an Olympics collectible scholar so I can't vouch for the veracity of such reports.The commemorative piece was a "Thank You" gift to those who purchased advance tickets to the Olympic Games.
The obverse of the medal depicts a dove (an international symbol of peace) holding an olive branch (another symbol of peace) in its beak, approaching the Olympic flame above the Olympic Rings logo. Below the rings is "1984" - the year of the Games - along with inscription of the two 1984 Olympics sites: Sarajevo and Los Angeles.
The medal's reverse features the logos of the two Organizing Committees (Los Angeles at the top, Sarajevo below ir), with bi-lingual inscriptions encircling the logos near the rim that identify each Olympiad.
The medal shown is 2-1/2" (64 mm) in diameter and weighs ~3.9 ounces (~110 grams).
It was struck in smaller sizes as well - I've also seem 19 mm and 35 mm examples (30 mm copper/copper-nickel versions are also known).
The medal I purchased came in a brown velour clamshell presentation case that was inserted into a white cardboard sleeve; I've seen other packages as well. It included a brief descriptive leaflet.
1984 Los Angeles-Sarajevo Olympics Friendship Medal
1984 Los Angeles-Sarajevo Olympics Friendship Medal - Descriptive Leaflet

For other of my posts about commemorative coins and medals, see:
Commems Collection