A basic translation would be that "man is always a muad." To begin to understand this idea we first need to learn what a muad is.
The basic focus of Bava Kamma is on damagers and their penalities. The Sages use an ox to represent one's property and then they explore innumerable ways that this property (the ox) can cause damage. In fact, they delineate three specific ways an ox can cause damage: shein, regel and keren. Shein (lit.tooth) represents possible damage that an ox does when it eats. Regel (lit. foot) represents damage caused when the ox walks. And keren (lit. horm) represents damage caused when the ox gores something with its horn.
Within the Bava Kamma each of these types are determined to represent a more general type of damage:
- Shein -- The act of damage that an animal does in the case of normal self-gratification.
- Regel -- The act of damage that an animal does in the course of normal movement.
- Keren -- The act of damage that an animal does with destructive intent and which is unusual for animals and their species.
So, if we return to the phrase -- adam muad l'olam -- and know that adam means "man or humankind" and l'olam means "always," we see that the phrase can be interpreted to mean that "humans are always warned ones." Another way of saying this is that we are "always responsible." In fact, in the Mishnah on daf 26a in Bava Kamma where this phrase is used, it goes on to say that humans are liable for damages they do whether awake or asleep, whether intentionally or unintentionally.
While the Talmudic Sages discuss this issue in amazing depth and detail, it is the online shiurim (lectures) on Bava Kamma from Rabbi Shlomo Singer from the PTI Yeshiva that have brought the importance of this idea most clearly home. As he stresses over and over and over again, if it is true that adam muad l'olam, then we have to be ever vigilant about each of our actions and each of our words -- we are responsible for the consequences. We are muad. We have been warned, so we have to focus much energy on our improving our character (our midos) to ensure that we do not hurt others with our actions or words.
Rabbi Singer does a wonderful job throughout his shiurim in bringing the often complicated Talmudic analysis into our everyday lives. And I believe that the phrase -- adam muad l'olam -- is a wonderful reminder to keep in our minds as we move about in the world and touch the lives of so many people.