One of the most funniest & yet important things of cricket is appealing. Appealing is nothing but asking the umpire to check if it is out or not by shouting “How’s that?”, appealing must be usually done by bowler. Appealing can sometimes win you matches, sometimes if umpire is in doubt regarding the decision may give decision in bowlers favour if the bowler’s confidence while appealing is very high. Appealing is not only bowler’s part, everybody in the bowling team can appeal the umpire.
Now coming to the other case if the original scenario is out & bowler doesn’t appeal for it, then the umpire doesn’t give it out because appealing is required from bowler is required for an umpire to check the delivery if it is out or not. Appealing is usually done in the case of run-out, LBW, hit-wicket, stumped & catch.
An appeal can be withdrawn also, there are many such cases in cricket where an appeal is made & umpire gives out, but originality is not out, then if fielding team withdraws the appeal then the batsman is called back to continue his innings.