A series is the smallest unit in the options world: one underlying, one type (call-option or put-option), one strike-price, one expiration-date. Every contract in a series is interchangeable, which is why they can be cleared and netted against each other.
Traders care because quotes, open-interest and volume are all reported per series. Two lines that look almost identical on an options-chain are separate series with separate books and separate liquidity.
Example: XYZ trading at $50. The XYZ 21 Mar $52.50 call is one series. The XYZ 21 Mar $52.50 put is a different series, and the XYZ 18 Apr $52.50 call is a third. If the March call shows 4,000 open-interest and the April call shows 60, the March line is the one you can get out of quickly.
Related: option-class, options-chain, open-interest, option-symbol