Reason for 2 cat5 cables to RJ11 Phone Jack?
There are multiple wires on the socket because it is a wired continuation on to the next RJ11 jack in another part of the house. In fact if you locate all the phone jacks in your house you will likely find them all connected together. The reason for this is because the wire set is capable of allowing for a landline phone to be moved from room to room OR for multiple phone sets to be installed. 

You would not want to use this wiring for an Ethernet type connection. For that  you will need to pull new cables from each location where you want to have an RJ45 back to a central location where you would locate a network hub or switch. The ease or difficulty of getting the new wiring in place will depend a lot on how your house is constructed and to some degree on the locations that you intend to locate the RJ45 jacks.