English Explanation of Mishnah Sanhedrin 4:2

In non-capital cases and those concerning uncleanness and cleanness [the judges declare their opinion] beginning from the eldest, but in capital cases they begin from [them that sit at] the side.
All are qualified to try non-capital cases, but not all are qualified to try capital cases, only priests, levites and Israelites that may give [their daughters] in marriage to priests.
Mishnah two contains more information regarding the differences between capital and non-capital cases.
This mishnah contains an additional two differences between non-capital cases and capital cases. (We learned of eight differences in mishnah one.)
In all types of non-capital cases the eldest judge may state his opinion first, but in capital cases the decision stating process begins from the side of the room, where the younger members of the court would sit. This is to prevent the youngest judge from being unduly influenced by the opinion of the eldest judge.
A person of any lineage may judge non-capital cases, even mamzerim (those born of illicit unions) and even converts. However, only those who can marry their daughters to priests, meaning priests, levites and Israelites can judge capital cases. This law certainly reflects the import that the Rabbinic society ascribed to familial relations.