Spider-Man is a teenage high school student named Peter Parker that receives his powers after being bitten by a radioactive spider. He's lived with his aunt and uncle since a young age ever since his parents died. Peter's powers give him the ability to cling to walls, and have the proportionate strength and speed of a spider. Along with that he gets a "Spider Sense" which allows him to detect danger and avoid it making it nearly impossible to hit him. Peter is also naturally very intelligent which is how he invented "Web Shooters" that allow him to swing from buildings and trap foes.
Batman is Bruce Wayne the worlds best detective and also a billionaire. The origin story of Batman changes very often, but one thing usually agreed upon is that a young age little Bruce saw both of his patents murdered which makes him want to put an end to crime in Gotham city. The most interesting thing about Bruce is that he doesn't actually have super powers. He is a normal person that is a master of stealth, extremely intelligent. He can also afford to create a seemingly endless supply of cool gadgets.
But who would win in a fight? This is an argument that I have gotten into on countless occasions with a surprising number of people. Spider-Man has always been my favorite superhero ever since I was a young lad so obviously I think he would beat Batman. However most people I come across do not agree with me. I attribute that to the movie portrayals of the two heroes. Batman's recent movies have been excellently done and are extremely popular, whereas pretty much every Spider-Man movie hasn't been too great.
Thanks to the internet questions like "Which fictional character would win in a fight" can be easily answered by people with more than me. Fortunately there is a youtube channel called ScrewAttack that does just that. The team takes the two characters makes stats for them and decides a winner. Afterwards they create an animation to show the outcome.