A baseball ball bat sweet spot is the exact point where you can smack the ball as hard as you like and all you feel is the rush of the swing and the sound through your ears. There has been a lot said about exactly where this spot lies on the bat. But truth be known, it's a different location on every bat.
Variations between wood, metal and composites can shift the spot dramatically. Width of the spot can also change. Manufactured materials seem to have a better consistency in the spot where wood can vary wildly from bat to bat; Even when turned on the same lath from the same stock.
The importance of not only locating but being able to consistently strike the baseball with that portion of the bat has two basic advantages. 1 when all the parts of the swing are aligned the sweet spot allows the maximum transfer of all that energy your collected up from your feet through your body. 2 it delivers a near painless vibration back through the batters hands.
Not only does mis-striking or being off spot dramatically reduce the energy transfer and subsequently how far the ball will travel, but it really can hurt.
So much thought has gone into the location and exploitation of the spot that even hard core physics gurus continue to study it. Http://www.physics.usyd.edu.au/~cross/baseball.html is just one place where they publish some pretty interesting things. I particularly like the graph of what a bat does during the process of the swing and contact. If you really want to spend a few weeks brushing up on the bio-mechanics of baseball http://webusers.npl.uiuc.edu/~a-nathan/pob/ has a bevy of links and references to keep your eyes blood shot For days.
Back to the matter at hand. How do you find the sweet spot on your baseball bat. T work. Set up a T at a nice level for a comfortable swing. Ditch the batting gloves and with a gentle swing, enough to knock the ball to 2nd or so, start hitting and concentrate on the 'feel' in your hands. It should not take too many strikes to figure out where the zone lies. Striking the ball on the inside or outside of the sweet spot will send vibration down the bat and into your hands. Search for the zone that sends the least vibration to your hands.
Next, mark from the inside to the outside of the spot with wide masking tape. Take a few more knock to confirm you have the spot. Now, with batting gloves on take full stride and swing at the ball. Take 5 or so then check the tape. Getting the picture. You have already determined where the spot is, now you are confirming what your swing is doing. Are the marks inside, outside or not even scaring the tape at all.
Not only does locating the sweet spot on your bat give you good information on what part of the bat you should be making contact with, but you now have solid information on what is happening when you swing at the perfect pitch.
You can also mark this spot with a permanent marker for later tape application. Remove the tape after each T session. Having glue build up on the baseball bat does nothing but make a mess and you do not want to inadvertently alarm an umpire to thinking something is up.