You can probably find a more informative post elsewhere. But long story short, deflectors buff science powers. The best way to see this is to go to space, press P to open your powers tab and find your science officer's powers. It will list which skills buff that power, so you will want a deflector that buffs some or all of the skills listed there. And that also tells you which science skills you may want to rank up for your captain's skills since that will additionally buff the science powers.
All the powers are like this, not just science powers, they are all affected by captain skills and any consoles that buff those skills, but deflectors also clearly have science skills on them.
So to think of it easier, if you have a phaser beam, you can buff that with 3 skills, energy weapons, beam weapons, and phaser weapons. Any consoles or other ship equipment that increase those skills helps buff your damage.
Similarly, science powers are all buffed by starship operations, then one of the 3 tier 2 skills like emitters, deflectors or sensors, and then a specific skill like sensor probes or astrometrics. Just check the power to see precisely which skills buff that power, and pick a deflector accordingly.
A good reference is to look for the Captain skill with the same name as one of the Deflector Attributes. This will give you which powers are effected by the attribute. This way you can have an idea prior to obtaining the BO skill.