A register in the context in music is very close to and can be thought of as a different way of talking about the range of an instrument, group of notes, ect. The definition of it is as follows:
In music, a register is the relative "height" or range of a note, set
of pitches or pitch classes, melody, part, instrument, or group of
instruments. A higher register indicates higher pitch. - Wikipieda
In the context of guitar and play chords it makes sense if you had two guitarist playing different voicings/shapes of the same chord to fill out the sound for a thicker texture. For example, if one guitarist is playing an open chord which would be in the lower register for a guitar the other guitarist can play up the voicing/shape up the neck to play in a higher register.
Let's look at a practical example. If someone instructed you to play an E chord, there are many ways to do it and just considering the 5 basic chord shapes we could play an E chord the following ways:
As you can see these are all E chords, but the are all a different set of notes and are all in a slightly different register. Have two guitarist play two different chord shapes produces a much fuller sound than the two playing the exact same notes.