The two LAN ports are for link aggregation. If your computer (usually a server) has link aggregation (also takes 2 LAN cables) and your NAS has link aggregation, they can transmit data over both network interfaces simultaneously, essentially giving you 2x the speed of your network. e.g. If your LAN is gigabit ethernet, or 1 Gbps, 2x link aggregation will allow you to transmit files at 2 Gbps.
The technology was made when HDDs first started exceeding 100 MB/s. But is a bit lackluster now that SSDs have blown past 500 MB/s. I think most people who need this stuff are looking towards 10 Gbps, either optical or ethernet.
If you don't have any other devices on your LAN with link aggregation, you only need to plug in one cable...