What does it mean and why is it so important? And if possible, how does one work on this.
The Maharsha refers to Raban Gamliel's dream cited a little later in the Sugya, concerning white (gleaming) barrels that contain nothing but ashes. Interestingly, the Mishnah in Pirkei Avos (4:27) expresses a similar thought when Rebbi Meir says, "Do not look at the barrel but rather at its contents" (see the continuation of the Mishnah there). So it is with people. There are some people who put on an air of righteousness but who are wicked inside. Hash-m is no more interested in their righteousness than you are in a beautiful barrel which contains only ashes. What we are talking about here is a person who lacks personal integrity. He acts as though he has certain qualities in order to fool others, but forgets that he cannot fool Hash-m. Most of us are guilty of this trait in some degree or other.
"Tocho k'Baro" means that he is totally honest in his behavior. The good that others see in him is genuine, and he practices it even when nobody is looking. This is best described as honesty and integrity. What one therefore needs to work on to attain it is the Midah (quality) of Emes, to learn to be truthful to oneself, inasmuch as if something is good to display to others, then it is also good for oneself.
In his second explanation, the Maharsha defines "Tocho k'Baro" as someone whose fear of Hash-m is on a par with his knowledge of Torah. Refer to the story of Raban Yochanan ben Zakai and his Talmidim on the next Amud (28b).
Clearly, "Tocho k'Baro" is not something that one can attain in minutes or even hours. It entails a lifetime of working on oneself. On the other hand, it is a fundamental Midah and well-worth striving towards.
B'Virchas Kol Tuv,