One of the most confusing concepts in Buddhism for many people is anatta, often translated as "non-self" or the illusion of self. This refers to the idea that you do not actually exist in the independent, permanent way that is commonly believed. All people and objects are actually ongoing interdependent processes that are referred to by name as if solid, but are actually always in motion.
Take for example the San Francisco Giants baseball team, which won the World Series last month and in 2010. The team in 2010 and 2012 had the same name "SF Giants" but was substantially different: almost all the field players had changed in these two years (though the bullpen was more stable). Even at the Giants victory parade for the 2012 World Series, several of the players were not sure if they would have contracts for the 2013 season and continue to be part of the team. So while the team may continue to play in the same ballpark, the "San Francisco Giants" refers to an ever-changing group of people with no inherent stability.
Even saying they play in the "same ballpark" can be called into question. The ballpark itself seems solid, but is also in continual flux, like all material things: the seats wear out and are replaced, the walls are damaged and repaired with new cement, the grass on the field grows, dies and is replaced with new sod. It too is not solid but a process. This is not just true of inanimate objects, it is true of your physical body, too: You are constantly taking in new air, nutrients and liquids, sloughing off dead cells, expelling liquid and growing new skin, blood, hair and nails. Your body too is a natural process, always in motion.
On the level of your thoughts, emotions and feelings there is never much stability either. A thought exists for a moment, then a new one arrives. Moods and feelings appear and disappear. Even when emotions or moods seem to stay for a while, there is constant variation in their appearance, just like clouds in the sky slowly changing and moving. We exist in constant motion and are impacted by everything around us. Our body is affected by what we eat, the air we breathe, the temperature and what we touch.
This is not just a fun thought exercise, but actually something that can change your life when you know this on a gut level. You will have less stress from resisting the change that is inevitable in life; you will be less surprised when things change or die, most importantly when you age or get sick.
Insight meditation provides the tools to know this truth regarding the illusion of self on a deeper than intellectual level, in a way that will change the way that we relate to our lives. Mindfulness can help develop wisdom that allows us to let go into the truth of the flow of experience. We allow everything that is ceaselessly in motion to be in motion, and enjoy the ride, since that is the truth of the way things are. So we can lead more happy and harmonious lives, whatever we work at or love -- including baseball!