Some sources say that 'so' and 'really' are intensifiers and the dictionary says 'so' and 'really' are adverbs, which leaves me confused. Are they intensifiers, adverbs or both? Are intensifiers a type of adverb? I am also confused as to how they can be adverbs because adverbs describe verbs and 'so' and 'really' describe adjectives instead of verbs. If they do describe verbs please give me some examples. I also want to know if I am getting the definition of adverbs confused. Do adverbs only describe verbs or both verbs and adjectives?
Assuming you only mean the senses of those words in which they intensify the meaning of another word (they each have other senses)…
Are intensifiers a type of adverb?
Pretty much. Now, there are different senses to words and disagreements about just whether something counts as an example of a word and so on, and this includes those words that are used to talk about other words.
It's perhaps better to think that by some ways of classifying words, they are adverbs, and by other ways of classifying them, they are intensifiers. Nor do you have to pick a side here, sometimes its more useful to use the classical classifications than other times.
… how they can be adverbs because adverbs describe verbs and 'so' and 'really' describe adjectives instead of verbs.
Adverbs modify verbs, adjectives or other adverbs. These more often modify adjectives.
If they do describe verbs please give me some examples.
As above, they more often modify adjectives, but really can also modify verbs.
While that can be really confusing [modifying adjective], I really like [modifying verb] that things aren't always in the neatest of boxes.