"Thank you for taking me into consideration" means thank you for taking time/effort/ to do something that involved you assessing me in some way.
It is often used in the context of a job search, as something you might write in a follow up letter to thank them for taking the time to give you a job interview, or you might write it at the end of an application letter for a job or scholarship or grant.
For example, more informally it means:
"Thank you for taking the time to read my application/conduct a job interview with me"
1:Thank you for taking me in consideration.
- This is incorrect.
2:Thank you for taking me into consideration.
- This is correct
3: Thank you for considering me
- This is correct but a more informal. It doesn't sound as professional. There is nothing wrong with it, but #2 above is the common 'professional' phrase.
Please also note: "under consideration"
This means something different: This phrase is used when you may write a letter offering advice on something (or perhaps a complaint, or making a submission to a working group) and they might reply "Thank you for your letter, we will take your advice under consideration."
This means they have read/heard your advice and will think about it ('consider' it) but don't make any promises as to whether they will actually use it or do anything about it.
It is often used in form-letters (e.g. standard letters used to reply to everyone) and cynical people think that using this wording more often than not is a polite way to say 'thank you for your advice, but we're not going to do anything about it'.
In the context of a job search or application they might say "Thank you for your application, we will take it under consideration" which means they will think about it but they do not promise you will be accepted.