I presume that you mean year, month and day are in different columns?
Then this might work:
DELETE FROM `logowanie_dj` WHERE CAST(CONCAT(dzien,':',miesiac,':',rok) AS DATE) < CAST('21:1:2014' AS DATE)
It creates a date value in the form dd:mm:yyyy
from the cells of the row and deletes it if it is before 21:1:2014
.
Please note that you obviously use some date format that is non-english. MySQL might have a problem with that, so that it could be you need to do this:
DELETE FROM `logowanie_dj` WHERE CAST(CONCAT(rok,'-',miesiac,'-',dzien) AS DATE) < CAST('2014-01-21' AS DATE)