In Heritage tab you can acquire more land using HP (Heritage Points). 1 HP can buy 20 land or forest or 10 mountains.

You can also spend HP to unlock research immediately.

These points will be renewed upon abdications and ascensions. The land acquired and research unlocked will be reset as well.

You earn HP through abdications and ascensions at certain populations. Note: It's the actual population which is used, max population is not taken into consideration.

Once the village have more than 50 population you will be awarded 1 xp for each additional villager.

The cost in xp of the next heritage point is 20+2*n with n equal to the total of hp owned.

hp_cost_in_xp = 20 + 2 * current_hp

xp_awarded = pop - hp_cost_in_xp_awarded_in_current_run - 50

calculateHeritagePoints( removeXP = false ) {
  let peoplePoints = this.resourcesService.getTotalPeople();
  let xp = this.xp;
  let threshold = 20 + (this.heritagePoints * 2);
  let pointsToAward = 0;
  while ( peoplePoints >= threshold ) {
    pointsToAward += 1;
    peoplePoints -= threshold;
    threshold += 2;
  }
  while ( peoplePoints + xp >= threshold ) {
    pointsToAward += 1;
    peoplePoints -= threshold;
    if ( peoplePoints < 0 ) {
      xp += peoplePoints;
    }
    threshold += 2;
  }
  if ( removeXP ) {
    this.xp = xp;
  }
  peoplePoints -= 50;
  if ( peoplePoints < 0 ) {
    peoplePoints = 0;
  }
  return { hp: pointsToAward, xp: peoplePoints };
}

peopleToNextHeritagePoint(): number {
  let peoplePoints = this.resourcesService.getTotalPeople() + this.xp;
  let threshold = 20 + (this.heritagePoints * 2);
  while ( peoplePoints >= threshold ) {
    peoplePoints -= threshold;
    threshold += 2;
  }
  return threshold - peoplePoints;
}

The formula for the population requirement where n is the number of HP earned: 100*2^(n-1)-50