The discussion about increasing the Bitcoin transaction per second started since the introduction of Bitcoin.
But on the 15th of August 2015 two long term Bitcoin developer Gavin Andresen and Mike Hearn released the BitcoiXT patch trying to solve this problem once and for all.
By applying this patch the Bitcoin Blockchain would increase the block size and therefore a hard fork of the main blockchain would be the result.
What is a hardfork ?
A hardfork is a change to the bitcoin protocol that makes previously invalid blocks/transactions valid, and therefore requires all users to upgrade.
Any alteration to bitcoin which changes the block structure (including block hash), difficulty rules, or increases the set of valid transactions is a hardfork. However, some of these changes can be implemented by having the new transaction appear to older clients as a pay-to-anybody transaction (of a special form), and getting the miners to agree to reject blocks including the pay-to-anybody transaction unless the transaction validates under the new rules. 
You'll find an ongoing discussion about the hardfork all over the Bitcoin community:
Bitcoin holders and speculators as well as Bitcoin traders are uncertain if the hardfork will occur. This uncertainty leads to a very volatile market and Bitcoin price is dropping as we see here:
What condition need to be need to be met in order to hardfork the Blockchain?
Once 75% of all Bitcoin miners agree to mine on the new BitcoinXT patch a grace period of 2 weeks starts. Miners, merchants and service providers then know to upgrade before the two week period elapses if they haven't already. Note that once the 75% threshold is reached the change is locked in and will occur after two weeks even if support dips back below 75%.
Do I get twice the amount of Bitcoins on both Blockchains ?
NO! You'll need to patch your Client in order to move the Bitcoins but you most probably not getting twice the amount of Bitcoins you own.
What are Bitcoin Mining-Pools are saying about the changes?
Fist of all we need to have a closer look at the distribution of mining-pools around the world.
Once a pool starts mining on the BitcoinXT patch it will count towards the 75% they need in order to hardfork.
BUT you need to know 5 of the biggest mining pools "AntPool, F2Pool, BTCChina, BW Mining, and Huobi" are based in China.
These 5 Bitcoin mining-pools have about 55% of all Hash-Power.
The mining pools came to the agreement at the National Conference Center in Beijing last Thursday. As they jointly account for some 55% to 60% of all hashing power on the Bitcoin network, it may now be increasingly unlikely that a consensus among the global Bitcoin community can be found on a block size increase to 20 MB.
They released a statement and a signed contract:
“After undergoing deep consideration and discussion, the five pools agree that while the block size does need to be increased, a compromise should be made to increase the network max block size to 8 megabytes. […] We believe that this is a realistic short term adjustment that remains fair to all miners and node operators worldwide.”
What does this statement mean for the Bitcoin community?
Most likely we won't see a change towards the BitcoinXT patch in the near future and hopefully the price drop on all Bitcoin markets will stop once every Bitcoin user, merchant has understood the message from the Chinese miners.
Check live here: https://getaddr.bitnodes.io/nodes/?q=/Bitcoin%20XT:0.11.0/
In order for you to make your own decision I have created a list of links about the ongoing discussion of the BitcoinXT issue:
You can use the "broken Bitcoin vs BitcoinXT" logo, but please send me some back-links or beer for it:
+-- Update: --+
August 24, 2015
The CEO of BitPay, Blockchain.info and 6 other CEOs of the Bitcoin community signed a statement which stated the BitcoinXT patch should be implemented.
We support the implementation of BIP101. We have found Gavin’s arguments on both the need for larger blocks and the feasibility of their implementation [...}