Sharing stock, also known as life stealing, is the action of transferring a remaining life to a fallen teammate who has no more lives. This puts the character back into action (at 0%), with one life, and removes one stock from a team member. This is initiated, by the defeated player, by pressing Start/Pause (A+B in Brawl) when out of lives. Naturally, this can only be done in a team stock match, where a teammate has more than one stock remaining. In Brawl, the narrator will announce "Share stock" when this is done.
If a team has three players, stock is taken from 1P, or in 1P's case, 2P. Assuming that the primary stock giver has been defeated, stock will be taken from the remaining teammate.
Strategy
While it may seem like a simple decision, many factors should be taken into account when choosing to share stock.
Firstly, it is wise for team members to discuss or ask permission before stealing a life, not only as it may be considered rude not to do so, but for strategic purposes. For example: If one were to steal a life from a teammate with two stock, but a high damage percentage, this would essentially be similar to swapping lives, as they're likely to be knocked off soon afterward. Of course, communication is not always possible during online matches, so sharing stock in these instances may be more of a personal decision.
One should also take the stage into account. Large stages like Hyrule Temple allow partners to survive to much higher damage percentages, while smaller stages like Final Destination don't.