What is the significance of using baseline pairs in radio interferometry? Radio interferometry utilizes arrays of smaller telescopes that are linked together to synthesize a larger aperture telescope. Astronomical radio observatories, such as the Very Large Array in New Mexico, consist of multiple radio antennas in various configurations (ie. 27 antennas for the VLA). When I read about the basics of radio interferometry, a lot of time is spent on the delay and baseline between a pair of telescopes. In other words, the light from the object will enter one telescope first before the other (unless pointed directly up) and a pair of telescopes act as 1 baseline. I don't understand the significance of these telescope pairs. Do the pairs act as a single pixel? I read that a pair of antennas measure one point in the u,v plane. Why are pairs of telescopes needed to do this and what is the significance to radio astronomy?
The basic idea behind interferometry is that of interference, the combination of two waves (in this case the electromagnetic waves from distant sources).  Interference inherently implies two signals to interfere with each other, and that is why the pairs of telescopes (also referred to as baselines) are important.  The interference pattern between the signals received at two different telescopes carries information about the spatial structure of the source.  Widely-separated pairs are sensitive to small-scale structure, and close pairs are sensitive to larger-scale structure (which is why you need both to reconstruct a good image).  North-south pairs are only sensitive to structure in the north-south direction, and likewise for other orientations of pairs, so again you need pairs/baselines oriented in different directions.  (The rotation of the Earth helps somewhat by changing the orientation of baselines over time, though modern interferometers with many telescopes, such as ALMA, have pretty good coverage in a single snapshot without waiting for the Earth to rotate.)
The signal from a source is recorded at each telescope, and then those signals are combined (or interfered) with each other for each pair of telescopes, and all of those per-pair interference signals constitute the overall data collected by the interferometer.  In a radio interferometer this interfering/combining of signals is done in a computer called a correlator. For radio, the signal at each telescope is converted to a voltage and these voltages are correlated; for an optical or infrared interferometer, the light from each individual telescope is split into multiple paths so that each pair of light beams can  be interfered directory in a beam combiner before the interference pattern is recorded.