I am aware that some books in the 5th edition of d&d needs board to be played on, but the cashier of the shop I was buying the adventure book (Hoard of the Dragon Queen) said that the adventure didn't need a board. And now, I'm a little bit confused over how that works. Because how is the combat going to work without a board to play the battles on?
No. You don't need a board for 5e.
5e is intended to be played however you'd like. Some groups (like the ones I GM), prefer to use a battle mat and minis to represent the play space. However, other groups have success either running the game entirely in their mind, or by tracking things much more loosely using pencils and graph paper, or just any kind of figures from approximation of location.
I've run 5e without miniatures and a grid before, and it's difficult, mostly because I and the group I was playing with was used to the prior edition that depends heavily on grids and minis. We adjusted, but it's a playstyle we were not used to.
So no you don't need a grid and miniatures to play 5e, they can be a helpful game aid, but are by no means required.
Players familiar with recent editions of D&D, tactical wargames, or most computer games are often used to combat systems where it is very important to know exactly where every participant in a fight is located at all times. This enables some very clever, tactical play from players who study their characters' combat abilities and can think quickly during combats. However, it is not the only way to run a combat, and D&D 5th Edition is less opinionated than other recent editions about how combats are orchestrated.
Theater of the Mind
A looser style of combat is often referred to as "theater of the mind", because much of the structure of the combat is left in the minds of the players rather than expressed with a grid. You're probably familiar with this style of play already, even, because it's how most groups run non-combat scenes.
The essence of running a theater of the mind combat is simplifying the hard-and-fast numbers of a grid combat into softer descriptions that we can easily imagine:
- Adjacent – Generally characters engaged in melee combat are adjacent. If one of these characters tries to back off, that would open up an opportunity attack, and area attacks that affect one of the characters have a good chance of affecting the other. Example: Two characters sitting next to each other at the bar in a tavern.
- Nearby – The characters aren't in melee, but are still pretty close to each other. Area attacks may be able to encompass both of them if targeted at a point between. If one of the characters decides to engage the other in melee, they will be able to approach and attack in the same turn. Example: Two characters sitting different tables in a tavern.
- Away – The characters are in the same general area, but not at all close to each other. Area attacks almost certainly can't hit both of them (though beam attacks may), and closing to melee range will take multiple turns of movement. Example: A character sitting at a table in a tavern and another character looking down from the upper level.
- Far – The characters are in completely different zones of the battle. Long range attacks may reach between them, but otherwise they are probably not going to fight each other at all anytime soon. Example: A character in a tavern and another character on the roof of a building across the street.
Even though this style is referred to as "theater of the mind", groups often play with some shared reference of where characters are generally located. This can be a sheet of paper with numbers and/or letter on it marking positions, spare dice laid out in the center of the table, or even figurines.
The key difference is in not sweating the details of where characters are. Rather than measuring or counting out squares, simply look at the positions and make a quick judgment call: going from point A to B, about how far will I get? Then just move the character and get on with play, thinking about those four positional relationships from above. Allowing the game to progress faster by relying on these quick rulings rather than focusing on exact measurements is one of the reasons some groups prefer this combat style to the use of grids.
Part of the intent of 5e was to do away with the need for minis and a battle mat. WotC knows that many RPGers from 2nd Edition on up are used to battle mats, but 5e is intended to break that trend. For us old timers who played AD&D and OD&D, the minis made it feel too much like War Hammer (which is a great game), but D&D is supposed to be played in your mind.