How did UV from the earliest stars 'alter the state of the 21 cm line' such that it shows up in CMB today? In this question I discuss the recent (open access) paper in Nature An absorption profile centred at 78 megahertz in the sky-averaged spectrum at length. The abstract begins:


  After stars formed in the early Universe, their ultraviolet light is expected, eventually, to have penetrated the primordial hydrogen gas and altered the excitation state of its 21-centimetre hyperfine line. This alteration would cause the gas to absorb photons from the cosmic microwave background, producing a spectral distortion that should be observable today at radio frequencies of less than 200 megahertz(1).


where reference 1 is Jonathan Pritchard and Abraham Loeb (2012) 21 cm cosmology in the 21st century. From there I've found Leonid Chuzhoy and Zheng Zheng (2007) Radiative Transfer Effect on Ultraviolet Pumping of the 21 cm Line in the High-Redshift Universe.

I understand some basics about the hyperfine transition in hydrogen, and that the "spin temperature" of a gas in space can differ from the temperature of other partitions if it's being pumped, but these papers are more than a bit hard to read.

Is there a simple way to explain the basics behind how the exposure of hydrogen to the UV light produced in early stars would cause the "blip" in the (now red-shifted) 21 cm part of the Cosmic Microwave Background radiation spectrum we see today?
The Intergalactic medium at the relevant redshift is made of neutral hydrogen. What we can measure is the brightness temperature (the temperature that the IGM would have if it emitted as a blackbody) relative to the CMB. This quantity depends crucially on the following expression:

$\frac{T_S - T_{CMB}}{T_S}$

where $T_S$ is called spin temperature.

The spin temperature is just a measure of the ratio between the number of hydrogen atoms in the first excited hyperfine state (spin parallel) and ground state (spin antiparallel).
It turns out that the spin temperature can be modified in three ways: one of them is Lyman resonant scattering (the other two are collisional coupling and scattering of CMB photons). 
Using atomic physics it's not difficult to see that $T_S$ is a weighted mean of the temperature of the CMB and gas temperature.

UV photons can change the spin temperature because a hydrogen atom in the lowest state, n=1 (if you are familiar with chemistry, a s state) with antiparallel spins, can absorb an UV photon and jump in a p (n=2) state, and then fall again in a s state but with parallel spins.
This mechanism is known as Wouthuysen–Field coupling.

Before the emission takes place, the gas is at the same temperature of the CMB and both are equal to spin temperature, so the relative brightness temperature is zero.
When Lyman alpha emission begins the spin temperature decreases resulting in the observed absorption peak. 
At some point the peak stops because the first stars emit X-rays and the gas becomes hotter than the background radiation.