Translation:I am washing the floor and father is washing the dog.
It is because the Finnish sentence ""Minä pesen lattiaa ja isä pesee koiraa" uses the partitive case (here, indicated by the double "aa" at the end of "lattiaa" and "koiraa") and in Finnish the use of the partitive case in a sentence like this indicates that the action is in progress (i.e., ongoing; not completed). In English, we use the -ing ending on the verbs to express the same idea: "I am washing the floor and father is washing the dog".
If you wanted the sentence to say "I wash the floor and father washes the dog" the Finnish translation would be a different sentence: "Minä pesen lattian ja isä pesee koiran." (Note that the ending -n has replaced the double -aa at the end of the words for "floor" and "dog": lattiaa has become lattian, and koiraa has become koiran.) So it is a different sentence in Finnish, just as it is a different sentence in English.
Minä pesen lattiaa ja isä pesee koiraa. = I am washing the floor and father is washing the dog. [Meaning for both languages: we are doing it right now.]
Minä pesen lattian ja isä pesee koiran. = I wash the floor and father washes the dog. [Meaning for both languages: we do it often, or regularly, or every Saturday morning, or whatever. But we aren't doing it right now. In Finnish it can also mean that we're going to do it in the future.]
"Minä pesen koiraa" = "I am washing the dog". The action is in progress, not yet completed. (This is also why I wouldn't translate this sentence as "I wash the dog", as someone suggested above. When you use the form koiraa it is specifically an action that is in progress right now; in English we using -ing on the verb for that.)
"Mina pesen koiran" = "I will wash the dog" or "I wash my dog [regularly]" = here you are talking about a completed action that will occur in the future or that occurs regularly. "I will [completely] wash the dog". "I [completely] wash my dog [regularly, often, on Tuesdays, etc]. It is not talking about what you are doing right now.