Party size is dependent on your Player Rank.
Party size limits how strong the heroes in your party can be. Each hero has a size. The stronger the hero, the larger their size. To fit heroes in your party, the total size of the heroes must fit the maximum party size you have. If you choose one very large hero then you might not be able to fit other heroes on your party.
Remember: many smaller heroes together are often stronger than one large hero. You should choose four smaller heroes that fit your party and keep the large hero safe for later when your party size has increased enough.Also note that higher star heroes have a bigger size, so evolving your hero to a higher form can make them not fit your party anymore.While strategically you'll always want to Level Up & Evolve all your Hero Cards, you might want to stave off an Evolve if it means that your Hero won't fit into your Party Size anymore.
You will be able to fit larger, stronger Heroes into your Party when you achieve a higher Player Rank, so let's go get that XP!