When we talk, there is always a syllable of each word where we emphasize the pronunciation. 

In Spanish, if the word ends in "n", "s", or a vowel ("a", "e", "i", "o", "u"), the emphasis in the pronunciation of the word is normally placed on the penultimate syllable. For example:

If the word ends in a consonant other than "n" or "s", then the emphasis in the pronunciation is normally placed on the last syllable. For example:

When the emphasis in the pronunciation of the word does not align with the previous two rules, we use an accent on the vowel of the "strong" syllable to indicate where we place the emphasis.

We can use the word “matemáticas” (maths) for example. This word ends in an “s”, so according to the original rules it should be pronounced matematicas, with emphasis on the last syllable. However, since you pronounce it differently, it has an accent on the vowel of that syllable. 

So how do I know which words have accents and which ones don’t?

There are some patterns we can identify. For example, a lot of words that end in -on or -cion have accents on that last “o”. Some examples of these words are:

Basically all the verbs in indicative past tense have accents for first, and third person.