A grid-tie hybrid system is a grid-tie system with battery back up. 

See Grid-Tie Basics

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With a grid-tie hybrid system, power from your solar array goes through a hybrid inverter, then it first powers your house, and next charges your batteries, finally if there is any excess power, it is "sold" back to the grid.  See Box A.

 

If you are not making power from the sun (cloudy or nighttime), then the grid supplies power to your inverter, which first powers your house, then charges your batteries.  See Box B

 

If the power goes out then your home will function as an off-grid home.  You will supply power and charge your batteries from PV if there is sun, if not, you will draw power from your battery bank.  

See Box C 

 

Most on-grid homes are not set up to be powered off of solar (they have things like electric stoves and electric hot water tanks).  For this reason, most people set up what is called an essential loads panel.  This means you are splitting your electrical loads into two groupings.  You will have two breaker boxes.  They will both be active when you are on-grid, but if the power goes out, you will switch to the essential loads panel, which will be powered by your batteries. 

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Then you can add in a generator, which will power your home and charge your batteries if you don't have enough sun.  But I'm not going to get into that here!

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Lest you think it is too complicated, the Sol-Ark hybrid inverter does almost all of the work for you seamlessly, once you are set up, and that is what we are for!