fMRI
Magnetic resonance imaging is a technology built upon knowledge of an intrinsic property of protons in hydrogen nuclei known as spin. Proton spin in hydrogen atoms behave like a bar magnet, and when exposed to the strong magnetic field of an MRI machine they align. MRI machines use electromagnets constructed from superconductive material, such as niobium-titanium, cooled with liquid helium in a vacuum chamber; this cools the material to absolute zero, reducing resistance to near zero. This allows for the production of the strong magnetic fields
Radiofrequency (RF) pulses can be used to knock the aligned dipoles perpendicular, after which the protons return to their alignment with the magnetic field (like really stiff bobbleheads). The return to position after the RF induces a measurable current, or echo, that is received by coils in the MRI. Coils closer to the body produce better images, stronger MRI magnets result in stronger echos.
An MRI sequence is composed of RF pulses and echos (in sequence). The time between is measured as the time to echo (TE). Because echos weaken over time, larger pulses are needed to 'reset' the strength of the echos; the time between larger RF pulses is known as the repetition time (TR). Variations in these timings allow for imaging of different tissues and fluids.
MRI coils that produces these frequencies are independent subunits of channels and process specific components of the MRI image. The components include amplifiers, filters, image processors, etc. The number of channels influences how much processes power in required during acquisition and also the resulting image quality. An analogy would be if you used several camera with various sensors to capture specific image properties, then stitched them together to make an ultra-quality image.

Larmor Equation: Magnetic field strength is proportional to the rotational frequency of hydrogen nuclei
Blood oxygen level dependent (BOLD) imaging is an indirect way of measuring brain activity in functional magnetic resonance imaging (fMRI). Active brain regions require increased oxygenated blood flow, and T2 weighted sequences can detect this change due to the different magnetic properties of deoxygenated Hemaglobin and oxyginated Hemaglobin.