It wouldn't be a new season of Fortnite without a brand new Battle Pass, but things work a little differently in Chapter 2.
This season, you'll be able to earn Medals to progress in your Battle Pass. There will be daily Medals to earn by completing certain requirements which will boost your XP and net you some cool rewards.
It works as a "Punchcard". Instead of daily missions, you have medal objectives which reward you with XP as you complete them. Each card is worth 2000 XP, except for the fifth and tenth medals which are 4000 XP apiece.
When you complete a challenge that would earn you a medal - for example, outlast 50 enemies. That medal is added to your daily Punchcard. During that match, you have the chance to level up that medal from bronze, to silver, to gold.
You then earn extra XP based on the level of medal.
Every day you can add 10 medals to your Punchcard before it resets the following day.
These can be things like "Visit named locations" and such. The punchcard is timed, and refreshes as the Season progresses.
Dataminer Lucas7yoshi appears to have found a challenge list of sorts that could be linked to the Medals, such as going fishing or chopping up wood.