Leagues are PoE trade currency game world variations that affect the way the POE game plays. There are lots of kinds of leagues, but not every type is available constantly. Despite the title, standard really isn't the most populated league.
Hardcore: Standard and other league variations can be played in Hardcore as well. This battles Path of Exile players to fill out the POE game without dying. In case you die, your personality is going to be demoted to the standard league. Be aware that hardcore leagues are more populated than non-hardcore leagues, and thus make it harder to set up and trade with other Path of Exile players. There are now no Xbox Achievements for finishing the POE game on hardcore, so only play hardcore in the event that you truly want the challenge.
Challenge: These offer special prizes for finishing league-specific challenges, with many challenges available to go after. These are generally available for three weeks, after that point any characters created for the battle league will be moved to the typical league.
Solo Self Launched: These league variants lock the cheap poe currency game to single Path of Exile participant, averting all trading and group. Naturally, this raises the challenge. Solo Self Launched leagues are not available on Xbox One at launching.