I See My Birthday Numbers Over and Over Again

It means you remember seeing your birthday numbers more often than you remember seeing other numbers that you see during the course of a day. Why People See Certain Numbers All the Time has more information about that.

People generally remember seeing numbers when they recognize the number as having personal meaning or emotional significance.

They see the number, make a mental note of it or remark to themselves that "oh, that number is …". Because they pay special attention when they see the number, they are more likely to remember seeing it.

Because people generally don't remember seeing the other numbers they saw during the day, they tend to think they didn't see those numbers.

It's a memory thing. The numbers you remember seeing seem to be the only numbers you see.