What's the determinant of the male-biased birth sex ratio in humans?
There are a number of ways in which the true sex-ratio at birth (let's assume the 51:49 is well estimated and is the true ratio) could deviate from 50:50. This list is just an brief overview.


Sex, in humans, is determined by the sex chromosome present in the haploid sperm cell which fertilises the egg. If males produced more or less Y-bearing sperm than X-bearing sperm, then the birth sex ratio would be expected to deviate from 50:50. However, studies suggest that sperm production is not biased towards X or Y bearing in humans.
The probability of fertilisation may differ between X- and Y-bearing sperm. If Y-bearing sperm were more likely to succeed in fertilising the egg then there would be a male-bias in the birth sex ratio. I've seen it suggested that the small Y chromosome makes the sperm slightly smaller and therefore faster, but can't find those claims right now. Regardless, it appears that sex ratio at fertilisation is not sex-biased.
Bias in the birth sex ratio can come through sex-biases in the failure rate in fetuses. If female fetuses are more likely to miscarry than male fetuses, over the course of the gestation, then the sex ratio at birth will be male-biased. It appears that there is sex-bias in the failure rate of fetuses which can be male or female-biased throughout gestation, but the tendency is for female-biased failure rate during the second trimester to generate an overall male-bias birth sex ratio.