Here is a complete guide to the map view display, showing how to see the map. It explains what each object is and shows other articles related to those objects.
There are 2 type of gyms: rival gyms and friendly gyms. Rival gyms are owned by rival team, and you can take over those gyms by winning gym battles. Friendly gyms are owned by a team you joined to. You can do 'training' in friendly gyms to increase the gym's prestige.
Additionally, you can have your own gym. By defense your gym longer, you can earn PokeCoins.
Pink flowers can be seen around certain PokeStops showing the PokeStop installed Lure Module. While the effect of Lure Module continuing, PokeStops release pink leaves.