Clash-of-clans – request and leave in Clash of Clans

You are determined offline when:

• The app is closed.
• The app is left inactive for 5 minutes.
• You are multitasking with Clash of Clans open in the background.

You are considered offline while the app is running in the background. You are also considered offline when you get the idle message:

EXP in Clash of Clans is pretty much like experience in any other game.
It can be found on the top left-hand corner of the main screen and profile screen.

The experience you gain then is placed alongside a level system, with EXP cut-offs, a number that increases as you increase your EXP, but the requirements to get to the next level also increases.

It basically shows how much a player has invested into a game. Or for most MMORPGs; their character.

You pretty much earn experience by:

• Upgrading Buildings
• Donating Troops
• Earning Achievements.
• Destroying townhalls in attacks
• Clearing plants/rocks from your village.

For all we know, there could be a Level 30 player with a Townhall Level 8 in Challenger League amongst all the Level 90+ players.

Answering your question:

It basically shows how much a player have invested into a game.

The only thing EXP is useful for is for unlocking decorations.
The more EXP you have, thus giving you a higher level, the more decorations you unlock.

If you need more information, you can find them in the Wiki:
http://clashofclans.wikia.com/wiki/Experience
http://clashofclans.wikia.com/wiki/Decorations