Noun: Intimate relationship.
Parisuhde is a compound word made from pari (“couple”) + suhde (“relationship”). Note: suhde by itself can also mean ”intimate relationship” or ”affair”, but parisuhde usually refers a recognized intimate relationship between two people.
Let’s translate the other word in the magazine headline, keeping in mind that like many headlines, this phrase is a fragment of a sentence:
Toimimaan is the 3rd infinitive of toimia in illative case. Toimia has many meanings ranging from ”to act,” ”to function,” ”to work” and ”to do.” (See more meanings in the sanakirja.org entry, and see toimia conjugated here.)
In our example, the best translation of this 3rd infinitive would be ”functioning” ”or ”working,” and in the illative literally ”into the functioning” or ”into the working.” In English, ”into” would not be used, however, as it sounds awkward.
The phrase might be best understood idiomatically if we consider the words ”miten saada” (”how to get”) might be missing, i.e. a more complete phrase might be ”Miten saada parisuhde toimimaan”, ”How to get an intimate relationship functioning.”