Shields are the main defensive equipment from Tyrian. Shields are the only things other than your armor keeping huge ionized beams from ripping into your ship and turning you into space bacon. Be sure to upgrade them whenever possible.
The shields power is indicated by a blue gauge on the bottom right of the screen during gameplay. Getting hit will deplete the shield power, but it will recover with time as long as you have enough generator power. If the shield's power gets depleted the player's craft becomes vulnerable to damage.