The timing correct feature will snap the notes of your performance to the time division that is selected.
1/4 puts a strong emphasis on each quater note. To better understand this, think about the rhythm of the kick drum in Stayin' Alive by the Bee Gees.
1/8 puts a strong emphasis on eighth notes. This time, think about the speed of the bass line in Billie Jean by Michael Jackson.
The rhythm of the Billie Jean bass line would sound like Another One Bites the Dust by Queen if the time correct feature was applied and set to 1/4.
1/16 will snap your notes to the same speed as the hi-hat groove in Basket Case by Green Day. 1/16 is used almost exclusively for hi-hats only.
1/32 and 1/64 are very fast; you will likely not need to use these divisions unless you want to create an incredibly speedy track.
The triplet button should not be activated unless you want to pack three notes into the space of two.
Keeping all of this in mind, it's important to try clapping along to your melody or beat before using the timing correct feature to determine which time division it falls into; you can do this by using the songs above as references.
Unwanted corrections will occur if the timing correct feature is turned on without first configuring these settings.
If you are certain that you have selected the correct time division, please make sure that Shift Timing is set to zero, as indicated by the yellow arrow below...