A phone line is 2 wires. Most houses are wired to support two separate phone lines, hence 4 wires. Given two cables you have for your phone jack, one is most likely the feed from the phone company and the second is a run to a second jack. Perhaps that second jack has been removed or just a blank cover was put ont the wall (older houses generally had a high mounted wall jack in the kitchen for a wall phone).
With old style phones, addktional jacks were added by "daisy chaining" from one jack to the other. You'd just match colors.
I'd look to see if you can find where the phone company wires attach to your house. Hopefully at that point, the 4 wire cable will be there and go to your jack. If so, then just remove the second cable with only the yellow and black wires. It is customary to use the red and green wires for your first phone line, so the DSL will probably use that. In that case, the yellow and black are unused, but could be used for a voice line if you wanted a second line from Century Link.
It sounds like you're getting Voice over IP (VoIP). Not sure if you want that or not, as there are pros and cons. They should be able to give you voice over the DSL line too with a filter. But you'd need a splitter at the jack to provide a jack for the phone. VoIP is fine too, and may be better for long distance calling. But if your power fails, your modem battery will only last so long before the internet (and your VoIP) stops working. This could be 1 to 7 days depending on how large the battery is and how much it degrades over time.