Correct spelling, explanation: even though the word is mostly known as a one-word, actually it stems from a plant name: a marsh mallow. Marsh, like a wetland, and mallow, like malva, a type of plant, which grew there. Originally this was what marshmallow sweets were made from, and now the conjoined words are mostly known as the confectionery rather than a name of a plant it derived from.

Definition of marshmallow:
noun
1. Soft sweets made from sugar and gelatin
The best part of any bonfire is toasting marshmallows.
2. A common name for a plant is Althaea Officinalis
Marshmallows, as the name suggests, usually grow in damp areas.

Incorrect spelling, explanation: Marshmellow would suggest that the word is made out of marsh and the adjective mellow. The soft sweets may make you think it’s correct, but it’s not, as the word actually comes from the name of the plant: mallow being a malva. This is why, in order to preserve the original meaning, the marshmallow needs to be spelled with an a.