How can a block regarded as confirmed in bitcoin? I am a little confused with confirmation mechanism in bitcoin PoW consensus.
According to bitcoin wiki:


  After a transaction is broadcast to the Bitcoin network, it may be
  included in a block that is published to the network. When that
  happens it is said that the transaction has been mined at a depth of 1
  block. With each subsequent block that is found, the number of blocks
  deep is increased by one. To be secure against double spending, a
  transaction should not be considered as confirmed until it is a
  certain number of blocks deep.


Let's say if A has 1 btc, and A sent 1 btc to B as transaction T1 and also sent 1 btc to C as transaction T2. It is possible that these 2 transactions are written into 2 different branches.  

In this scenario, if miner M1 keeps mining based on branch with T1 and M2 keeps mining based on branch with T2, finally subsequent block for these 2 branches will more than 6, and in most of apps these 2 transactions will be regarded as legal. I am thinking there might be other verification to make a block regarded as confirmed. 

My question is: what makes a transaction confirmed? Thanks in advance.
Let's say if A has 1 btc, and A sent 1 btc to B as transaction T1 and also sent 1 btc to C as transaction T2. It is possible that these 2 transactions are written into 2 different branches.


Yes. That's possible.

But there is still no double-spend because only 1 branch will be the accepted one in the future.

Assume that there are more miners. If miners 3, 4, 5 and 6 start mining on the second branch, it grows faster.
After 2 hours, branch1 has 1200 blocks, but branch2 has maybe 1209 blocks.
The chain/branch with the most block is the relevant chain. So miner 1 does not even want to mine on his branch anymore because he knows that the others will ignore this blocks 1201, 1202, 1203.
So miner 1 also switches to branch2 because otherwise, the only wastes electricity.