Translation:My husband likes this description.
You have to say "a mi esposo le gusta". Here "a mi esposo" and "le" make the same syntactical function (indirect object), thus it's somehow redundant information. You can omit "a mi esposo" if you assume it to be known and say "le gusta", but you cannot omit the pronoun and say "a mi esposo gusta".
In your second case it's the same. You can say "me gusta" or "a mí me gusta" if you want to put more emphasis, but never "a mí gusta". Notice the accent in "mí" because it's a different word than the possessive "mi" as in "mi marido".
you need the 'a' in 'a mi esposo le gusta.' ==> This description is pleasing TO my husband. The prepositional phrase "a mi esposo" clarifies who the 'le' is referring to. Without the 'a' (which is not the personal 'a,' but the actual prepsotion "a') it is no longer a prepositional phrase