Mathias is a Maltese Christian who's in l-o-v-e with Abigail. Even though his mother, Katherine, isn't keen on having her son marry a Jewish girl, Mathias is still dead set on marrying his daughter.
Our boy Mathias has the rare distinction in this play of being totally innocent. Really—this guy doesn't do anything wrong; he just gets caught up in Barabas's plots. Out of Mathias and Lodowick, it's Mathias's death that matters more. When Abigail finds out about how the two men died, she gets a little ticked off at her dad:
Admit thou lov'dst not Lodowick for his sin,
Yet Don Mathias ne'er offended thee.
But thou wert set upon extreme revenge
Because the Prior disposed thee once,
And couldst not venge it but upon his son,
Nor on his son but by Mathias's means,
Nor on Mathias but by murdering me. (3.3.40-46)
In other words, Abigail points out that Lodowick was understandably on Barabas's hit list because he's the son of hisenemy Ferneze. With the murder of Mathias, though, Barabas is really crossing a line from the land of reasonable revenge to this scary other place where nobody, including Abigail herself, is safe from his plots. So, poor Mathias is basically there to (1) make us feel really sorry for Abigail, and (2) show us how cray-cray Barabas is.
Sorry, dude. It was good to know you.