bioinformatics - What is the potential function of ultra-conserved elements in the genome?

Probably development, in particular transcriptional regulation. To quote each link in turn,

They are found in clusters across the human genome, principally around genes that are implicated in the regulation of development, including many transcription factors. These highly conserved non-coding sequences are likely to form part of the genomic circuitry that uniquely defines vertebrate development.

and

[Highly conserved non-coding sequences] are significantly associated with transcription factors showing specific functions fundamental to animal development, such as multicellular organism development and sequence-specific DNA binding. The majority of these regions map onto ultraconserved elements and we demonstrate that they can act as functional enhancers within the organism of origin, as well as in cross-transgenesis experiments

Additionally,

Here we report that 45% of these sequences functioned reproducibly as tissue-specific enhancers of gene expression at embryonic day 11.5. While directing expression in a broad range of anatomical structures in the embryo, the majority of the 75 enhancers directed expression to various regions of the developing nervous system.

These regions tend to be highly clustered in around 200 areas, and most of them are non-coding. ncRNA is often regulatory, and those UCE clusters are associated closely with developmental genes. That being said, not all of them are clustered near known genic regions, which might be a good indicator that there are heretofore unknown genes in those areas; UCEs might be useful for discovery. And here's a paper trying to give a role to one in cancer.