So from my understanding there exists a photometric system in Astronomy, such that a particular letter such as I corresponds to the I band (with I meaning infrared), and corresponds with 806nm effective wavelength with a bandwidth of 149nm. Does the filter, filter everything outside the range; of the effective wavelength plus/minus half the bandwidth. And only E-M waves within the desired range are caught. Please let me know if anything of what I said above is incorrect. Thank you.
That is essentially correct. Photometric surveys usually use a few bands (I.e. SDSS uses the $ugriz$ set of filters) where each band covers a different portion of the EM spectrum, but these portions overlap. The overlap is handled differently depending on the specific survey we're interested in, but is part of the physical systematics that the apparatus must take into account. There are a slew of systematics involved with actually modeling how the detectors parse the photons that are captured by the filters, which I will not get into here. SDSS has great documentation, so explore it and then ask more specific questions when you have them. http://skyserver.sdss.org/dr2/en/proj/advanced/color/sdssfilters.asp
This website has some great info on the basics of photometry. http://slittlefair.staff.shef.ac.uk/teaching/phy217/lectures/principles/L04/index.html