From LBPWiki

Downloadable content • •

Downloadable content (DLC) are game add-ons that are available from the Playstation®Store, which can be easily accessed from the in-game LittleBigStore. You will find everything from additional costume pieces, stickers, objects, decorations, and music. Additionally, there are downloadable level kits that may include a combination of new gaming elements, additional playable levels, themed stickers, themed decorations and more!

"Because LittleBigPlanet is an ever changing world, bustling with creativity, and with new things to see and do every day, we like to keep adding things to the game to inspire all you wonderful Creator Curators out there. This is a big list of those things. You can dress your Sackboy up as some of our favourite video game, film or comic characters, or in special seasonal outfits. We’ve added fun new levels to play with game changing powerups, and new creative tools, stickers, objects, decorations, music and more. All of them can be bought or downloaded for free from PlayStation®Store! Well OK, ya got me, some can’t be because they’re contest prizes or special community rewards, and some are only released when the time is right! We could hardly have people downloading a Santa costume in the middle of summer now could we? Let chaos reign supreme? No thank you!"

from http://www.littlebigplanet.com/en-gb/game_guide/ps3/downloadable_content/

Limited access rules to not owned DLC

Through they are called "downloadable", DLC data in LBP is actually downloaded with game updates (or in later editions of the game they can be contained on the game disc) and by buying DLC you only unlock the content for your personal use. This is because not owning an item of DLC in LBP doesn't restrict access to DLC used in others' creations and to online friends who don't own the same DLC, both in costumes and co-creating. This limited access to DLC has a specific set of rules:

• During an online session players have limited access to DLC that the current host owns.
• Any player can freely play any community level containing DLC that they not own.
• If a level copied or placed from someone else's back-up to the moon uses any DLC that the current host of the game doesn't own, that level can be only accessed in play mode.
• The player can collect, receive or capture objects containing DLC that they don't own, but they can't use them in create mode until they buy (or the current host of the game owns) all DLC used in object.
• The host can play a level from a Premium Level Kit that they own with online players that don't own the Premium Level Kit.
• Despite this, trophies that are part of that Level Kit won't be unlocked for a player who has bought the DLC, even if they are achieved when playing with someone who owns the Kit. Item collection, however, does work, but items will be unusable from Popit until the DLC is purchased.
• The player can collect items from DLC levels that they don't own, and the items appear in his Popit; but, similarly to community objects, they can't use them in create mode, until they buy DLC used in that level (or the current host owns it).
• The player can't wear costume items and outfits containing DLC that they don't own, even if the current host owns them.
• After 1.05 update of LBP2, you are able to edit an level with un-owned DLC, but not able to copy them and use them more times.