There are many ideas surrounding this idiom but the most plausible seems to be related to actual mustard.
There has been an association between the heat and piquancy of mustard and the zest and energy of people's behaviour. This dates back to at least 1672, when the term 'as keen as mustard' is first recorded. 'Up to mustard' or just 'mustard' means up to standard in the same way as 'up to snuff'. 'Cutting' has also long been used to mean 'exhibiting', as in the phrase 'cutting a fine figure'. Unless some actual evidence is found for the other proposed explanations, the derivation of 'cutting the mustard' as an alternative way of saying 'exhibiting one's high standards' is by far the most likely.
Read more about this idea and the other ideas here.
But what does the phrase mean? It means something or someone is successful and has risen up to high expectations.