Stacy McGaugh's latest post at his Triton Station blog explains why Big Bang Nucleosynthesis (BBN) poses a challenge to the LambdaCDM Standard Model of Cosmology.
Basically, BBN favors a lower primordial baryon density as of the time of nucleosynthesis, while the cosmic microwave background (CMB) astronomy data when interpreted in light of the LambdaCDM model in a model-dependent way, favors a primordial baryon density as of the time of nucleosynthesis that is two times higher.
But, there are lots of technical issues that make the 4-5 sigma discrepancy less obviously an irreconcilable conflict than it might otherwise seem to be.
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