Because this question has proven a little more derisive than I had anticipated (where's that engineering sense of fun/humour?)- I thought I'd attempt an answer as well, if only to prove it's an engineering question which can be answered using the engineering method; although hopefully someone using something more than Google will be able to chip in with a much more informed answer...
I'm definitely not an electronic engineer- but as I see it, sooner or later this question comes down to:
$$E = CK$$
Where
- $E$ is electric energy stored/used by the phone
- $C$ is a constant determined by the efficiencies of converting, storing and transfering the original kinetic energy to the electric energy.
- $K$ is the original kinetic energy generated.
It turns out that kinetic energy harvesting is actually a major field of research and development (especially with the dawning advent of wearable tech) This article states that intentionally shaking an object (which, we could call analogous with the band's usage) could generate something in the region of 3 milliwatts.
According to another forum (which I admit isn't the best reference); there are very few losses in the conversion of kinetic energy to electricity- so around about 95% of the 3 mW will be converted.
A lithium ion battery has around 80-90% charge/discharge efficiency; which means that 90% of 95% of the original 3 mW will make it to the phone.
This means that the energy given to the phone by the band is:
$$ E = (95 \% \times 90 \% ) \times 3\text{mW} = 2.565 \text{mW} $$
Apparently an iPhone battery holds around 5 watt hours.
This means that the band would require:
$$ \frac{ 1 \text{W} \times 5 \text{hours} } { 2.565 \text{mW} } = 81 \text{days} $$
However, I'm guessing it was never designed to be the primary power source- and looking at the same reddit post quoted for the battery capacity- it seems that the minimum delivery to keep your phone going (i.e. standby power usage) is 21.8 mW; which means that there's a 7:1 ratio of generation to usage time (let alone the suggestion of the same article that 1W is required to register as 'charging').
From researching the answer to this question- I'm beginning to think it's just a hoax for a bit of marketing exposure- but I'll be the first to admit that electricity and its generation is far beyond my training as a structural engineer; so maybe someone will correct me?