In the context of NGS analysis, consensus sequences provide regions where we can make confident calls, which is missing from variant-only VCFs. They are mostly useful for popgen. For example, you can compute heterozygosity from a consensus sequence, but you cannot do the same with a variant-only VCF.

I think consensus sequence represents which amino acid or nucleotide appears the most frequent in a position. I have seen it used most during estimating motifs and also after multiple alignment. And most of the splice sites are represented by consensus sequences too.

A typical consensus sequence looks like this:

AG[TC]T[CG]NSA

And I'm not sure about the vcf files question. It depends on the kind of analysis you are doing and why you need it I guess.

A motif usually has a consensus sequence with high information content at most bases. One could use a consensus sequence to demonstrate that a set of genomic regions (obtained via lab or computational methods) constitutes a particular motif.