Basically, it is conceded that the player tabbed the "franchise player" is going to sign a large contract, either from his team or through free agency. But by tabbing him this, if the player doesn't resign with the original team, they are guaranteed some sort of compensation (draft picks) when their player chooses to sign elsewhere. (see Mr. Bond post)
How does this help? Teams trying to sign the franchise player of another team will need to assess whether the high salary + the loss of draft picks is worth the risk. The original team has a higher chance of retaining their own players.
In basketball/baseball, you'll often see teams trading players (with contracts that expire after the current year and will unlikely resign with the team in the offseason) right before the trading deadline. Often, the team will receive less than equal value in the trade. This must occur because they don't have the "franchise player" option at the season end that guarantees them any extra compensation. Therefore, it's better to unload a player through mid-season trade in exchange for less value than lose him in the off-season and get nothing in return.