"A," "An," and "The" are all articles. It is easy to explain the difference between them, but it is difficult to explain when they are used.
"A" and "An" have the same meaning. They are both indefinite articles. They are only different depending on what word or sound is following. Here is a brief explanation.
You should use "A" when the following word starts with a consonant.
"A dog..."
"A boy..."
"A building..."
"A hamburger..."
You should use "An" when the following starts with a vowel sound.
"An eagle..."
"An umbrella..."
"An elephant..."
"An awesome book..."
"The" is a definite article. The difference is if the noun or subject you are talking about is specific or not. Examples are the best way to understand the difference, so let's take a look.
If you say, "I am going to a library to study," then the person you are speaking with does not know which library. If you say, "I am going to the library to study," then the person you are speaking with knows the specific library you are going to.
"I am going to a coffee shop" (No specific coffee shop)
"I am going to the coffee shop" (A specific coffee shop both the speaker and listener knows)
Here is a slightly different example, but still using the same concept of specific or general.
"I am going to sit in front of one of the computers in the lab"
"I am going to buy a computer"
Although the computer in the lab can be one of many computers, the correct article is "the" because it is still a specific computer that exists in the lab. However, if you say you are going to buy a computer, you cannot use "the" unless you already have the computer specified. Buying a computer can be any brand, type, or size so it is very general. Therefore, you must use "A" in this type of sentence.
Here is another type of example:
"The heat wave is unbearable"
"I heard a heat wave is coming"
The difference between these two sentences is that the "heat wave" is specified in the first sentence, and not specified in the second sentence. In the first sentence, the heat wave is already present and both the speaker and listener knows that the heat wave they are talking about is the one they are currently experiencing. The second sentence is referring to a future heat wave that is not specific.
When and When NOT to use an article
One common rule to keep in mind is that articles are not used when referring to a name."Turn right at the burger store"
"Turn right at McDonalds"
"The boy was running very fast"
"Mike was running very fast"
Another example of when not to use an article is when referring to general things in conversation.
"Too much alcohol is bad for you"
"Cigarettes can cause lung cancer"
When you are referring to sports, you do not need an article.
"I love playing badminton"
"Football is a dangerous sport"
In most cases, you don't need an article when referring to a country except when the name is referring to multiple countries or regions. For example, if you say England or Scotland, you don't need an article, but if you are referring to The United Kingdom, then you do need an article.