Some forms of ser are cognate with "essence", but ser itself is not.
Ser in Spanish is a "suppletive verb", which is missing some of its forms and has stolen them from other verbs to compensate. Compare English "go", which doesn't have the past-tense form *goed; instead, it's stolen the past form "went" from the unrelated verb "wend" (as in "wend your way").
Ser itself comes from Latin sedēre "to sit" (*). (Estar on the other hand is from stāre "to stand".) English has various cognates of sedēre, but "essence" isn't one of them.
However, forms such as the present-tense soy, es, somos, son come from the Latin sum, es, sumus, sunt: the present indicative of the verb esse, "to be". "Essence" and related words do come from esse; the participle ending -nt- was added to esse to form a word meaning "being". Thus "essence" is "that which is being", and "essential" is "related to essence", and so on.
As far as the noun ser, I'm afraid I don't know its etymology, but I'd assume it's related to the verb.
(*) The etymology I'm familiar with is sedēre > seder > seer > ser, though as pointed out in the comments it could also be from esse > essere > esser > ser. Most likely the two forms influenced each other, because there are some forms of ser that are definitely from esse and others that are definitely from sedēre.