I've covered some of the basic theories in this earlier post. I would also recommend the Ruggles and Saunders article that I reference there.

To reiterate a point from both of those, the largest difficulty of interpreting the lines is not their scale or their "mystery:" it's their simplicity. The more complex and involved something is, the more we can tell about its production and purpose. A typewriter, for instance, has a single, very obvious purpose. A piece of string, however? How does one date a piece of burlap cord, and what's its purpose? The typewriter's complexity creates a very narrow solution space.

That said, we can date the lines. Basic stylistic comparison connects them with the local Nasca culture and their Paracas predecessors. The motifs of the figural lines appear in the pottery and tapestries of both groups. This is confirmed by absolute dating methods. Radiocarbon dates from associated archaeological sites center around 400-650 AD. Dates from organic material trapped in desert varnish are between 560-660 AD. Thermoluminesce dating gives similar results. These correspond to dates from other Nasca culture sites, so the affiliation is a sound consensus.