I've seen a bunch of questions on this subject but no answers. See Meaning of LED Status Indicators - Verizon Wireless Network Extender - 1X/EvDO/Business | Verizon Wi... for the technical answer. The green indicator indicates "1xRTT is in-service but EvDO is in error." You can refer to Evolution-Data Optimized - Wikipedia, the free encyclopedia and CDMA2000 - Wikipedia, the free encyclopedia for a more complete explanation of the terminology. In short, if your SYS LED is solid green you probably have voice communication with the Verizon network, but if you also have 3g or 4g service, your data connection may not work properly. If your mobile phone is connected to your LAN via wi-fi then this may not matter.
This condition occurred on our network extender after rebooting our router, which is a dual-NIC computer running Ubuntu Linux. When the router came back up after a minute or so the SYS LED on the network extender had switched from blue to green, and remained so until I power-cycled the network extender. After the usual connection and settling process all four LEDs came up solid blue
I should add one more thing. The web page at Meaning of LED Status Indicators - Verizon Wireless Network Extender - 1X/EvDO/Business | Verizon Wi... is poorly formatted for web viewing. Copy the entire page from the title ("Meaning of LED Status Indicators ...) through the last line of the normal startup progression list and paste it into a spreadsheet such as Excel, or even into a word processor such as MS Word or Libre Office. You'll get a nicely formatted tabular document which can be easily manipulated for best readability. You can print this document out and keep it with the documentation on your Samsung network extender to supplement the "Quick Start Guide" document which came with it.
This accomplishes two things. It provides you with a concise, well formatted document describing the states of the network extender and its connection to the Verizon network, and should Verizon decide to remove this document from its website you'll have a permanent copy as long as you have this device.