Translation:The smoke that comes from the church is white.
Both Danish words translates to “that”, but in different capacities.
Here, “that”/“der” is a relative pronoun that refers back to “røgen” in the main clause and serves as the subject of the relative clause that it introduces— “der kommer fra kirken”. This relative clause narrows down which smoke we are talking about.
Here is an example (from the Conjunctions Lesson) of “that” as a subordinating conjunction “at”:
Jeg støtter at hun arbejder. (I support that she works)
This word also introduces a clause (a subordinate clause), but it does not refer back to an antecedent noun (so it is not a pronoun). Structurally it is just a glue between two clauses and does not also serve as the subject or object of the sub-clause, as would be the case with a relative pronoun.
As relative pronouns both "der" and "som" can be translated as "which" or "that". If the pronoun is the subject of the clause, both can be used: Jeg kender manden der bor i dette hus / Jeg kender manden som bor i dette hus. It the pronoun is an object (there is another subject), only som can be used: Jeg kender manden som du talte om. (You cannot say: * Jeg kender manden der du talte om.) As far as I know, Danes prefer "der" when it is possible to use it. "Som" is used more in written language. (I am not native, so Danes may correct if I am wrong.)