If fungoes are a ball tossed into the air by a batter and then struck as it comes down then a fungo bat is a baseball bat used for hitting fungoes. To go into more detail, a fungo bat is a long, lightweight baseball bat used by coaches (or parents) during pregame hitting or practice to help them hit grounders and pop flys with more consistency and less fatigue. To be one of the best in baseball, countless hours of practice are a must and fungo bats are intended for both infield and outfield practice. Plus, they help tremendously with control and accuracy so that coaches and parents can place a ball where they want when they want. 
Baseball bats are made of either wood, or a metal alloy (typically aluminum). Most wooden bats are made from ash. Other woods include maple, hickory, and bamboo. Hickory has fallen into disfavor over its greater weight, which slows down bat speed, while maple bats gained popularity[5] following the introduction of the first major league sanctioned model in 1997. The first player to use one was Joe Carter of the Toronto Blue Jays.[6] Barry Bonds used maple bats the seasons he broke baseball's single-season home run record in 2001, and the career home run record in 2007.[6] In 2010, the increased tendency of maple bats to shatter has caused Major League Baseball to examine their use, banning some models in minor league play.[7][8]
A fungo bat is a specially designed bat used by baseball and softball coaches for practice. The etymology of the word fungo ( /ˈfʌŋɡoʊ/) is uncertain, but the Oxford English Dictionary suggests it is derived from the Scots fung: to pitch, toss, or fling.[26] A fungo is longer and lighter than a regulation bat, with a smaller diameter. The bat is designed to hit balls tossed up in the air by the batter, not pitched balls.[27] Typical fungo bats are 35 to 37 inches (89 to 94 cm) long and weigh 17 to 22 ounces (480 to 620 g). Coaches hit many balls during fielding practice, and the weight and length allow the coach to hit balls repeatedly with high accuracy. The small diameter also allows coaches to easily hit pop-ups to catchers and infielders along with ground balls due to better control of the barrel of the bat.
Secondly, the first base fungo hits balls to the third baseman, who turns a double play with the second baseman to the normal first baseman, while the third base fungo hits balls to the shortstop, who throws to a shortened deep firstbaseman (this means that the deep firstbaseman stands closer to the shortstop than normal, so that the throw across this infield is the correct distance - this does NOT mean that the deep man stands any closer to the normal first base position - this length should always be sufficient)
For starters, we should clarify just what we’re talking about when we say fungo bat. Longer, lighter and thinner than a regulation bat (but a larger barrel), a fungo bat is typically 35 to 37 inches long, and weighs between 17 and 22 ounces. As David Allison wrote in the June 1978 edition of Country Journal, “A fungo bat looks to be a cross between a baseball bat and a broomstick.”