In addition to the low-bandwidth pointed out by other commenters, the burden on NASA's Deep Space Network a significant limiting factor [1].
The DSN is the only system of antennas capable of communicating with New Horizons at its current distance, and shares the responsibility of communicating with many other deep space missions.
So, aside from having a bandwidth on the order of 1 kb/s, New Horizons is also going to have to wait in a queue of other missions waiting to use the DSN.
If NASA approves additional funding for NH next year, it will be flying by another Kuiper belt object in a few years. It looks like either 2014 MU69 or 2014 PN70.
They are gathering a lot of data but their transmission speeds back to Earth are very slow. They are also including a lot of redundancy in their transmission from what I understand, since there is a several year window to transmit so they might as well use it.
Adding to that, it will take time to develop models that can explain these unexpected features! Even with all the data in hand, it may take a number of years of intense study and perhaps simulation to make a convincing case for any single explanation.
It’s their way of implying that this mission will provide enough data to lead to interesting discoveries for years to come. Data on its own is useless, someone actually has to look at it and interpret it and pick out what’s interesting and what’s not and all that.
Obviously in this forum everyone jumps to the technical explanation (slow data transmissions!) but that is exactly not it.
For one thing the data is sent back very slowly. Estimates are that it will take New Horizons roughly 16 months to send it all back.
Then you have to sort through and analyze it and use it to verify predictions formulate new hypotheses and so on. The data will still be impacting scientific progress for years after we get it all and sort through it.
why will it take years?