From the Super Mario Wiki
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Big Stars are Stars that appear in New Super Mario Bros.. They are only found in "Mario vs. Luigi" mode, and a set amount of Big Stars must be collected to win. Whenever a new Big Star is collected, everything in the level is reset.
In the settings for the game, the host player will decide how many Big Stars are required to win the battle. The options are 3, 5, and 10. Also, at the top of the upper screen, the amount of Big Stars a player has is displayed above his or her character. When a player collects the second last star they need, the stars in the star counter will start pulsing and the music will go faster until the last star is collected. The location of the Big Stars are seen in the touch screen.
One Big Star at a time appears in the level until it's collected. After players have collected at least one Big Star, players can make each other drop Big Stars (if they have any) by jumping on them, hitting a block when the other is standing on top of it, or attacking them with a Fireball, Shell Dash, etc. Players can drop Big Stars by touching an enemy, falling into a bottomless pit, or getting crushed by walls. Ground Pounding or Drill Spinning into a player can make that player drop three Big Stars. If a Big Star is dropped, it will start bouncing around until it is collected, falls into a bottomless pit or it will disappear. Collecting a player's star will not reset the level. Silver Stars have similar movements but there are five in every level.