Consider the sentence
我出发了。
with the translation
I'm leaving.
This was given to me in a list of examples demonstrating the putting 了 after a verb expresses a completed action (perfect aspect, I guess). But in this particular example the action isn't completed. So then why does 了 belong here? How would the meaning change without it?
I'm leaving is rather ambiguous; going from English to Chinese, it is either
我出發了 is also ambiguous; going from Chinese to English, it is either
Context is essential; if 我出發了 is translated to I'm going to leave, then「了」is used as a function where it is put at the end of a sentence to declare (to a listener) the beginning of an action. In this sense, we have:
It is mandatory to drop「去」in verbs which involve going/leaving anyway, such as「走」and「出發」. In other verbs, including「去」is optional, but it reveals the sentence structure better. You can see that in the written language, without explicitly writing「去」, it is hard to see that 我吃飯了 is a declaration of I'm going to have food, but in spoken language the context should be clearer.
How would the meaning change without「了」?
It is ungrammatical to say just 我出發, like it is ungrammatical to only say in English I leave.
我出发了 can be taken as the shorthand of 我要出发了. The literal translation can be: I'd be leaving. 了 denotes a completion state you would enter in the very near future. E.g. 我走了， I'd be in the 'gone' state in a second(or just right now), that is, I'm going. By the same token, we can translate 我出发了 as I'm leaving.
In practice, people say 我走了， often accompanying with their actions: stand up and walk away. It means I've decided to go and I'm doing it(going).
You are with me. You want to go. You say: 我走了。
You and I have an appointment in a restaurant. You are late. I call you. You say: 我已经出发了。
我走了。 I'm leaving.
我出发了。I already left. (I'm on my way to the restaurant)
The difference is, whether or not you are talking to a person face to face, 我走了，or you are on the phone, 我（已经）出发了。
出发：leaving with a specific destination in mind 走了：leaving
我们出发了。：Let's go.
我们走吧。：Let's go, let's leave.
The problem arises with English. English and its predecessors maintain there is a thing called Tense. Thus, English speakers look at Chinese and want to find Tense. Language is more complicated than that.
My advice: do not even try to match Chinese to Western Grammar concepts. Tha past was never perfect, forget it.
了 means something you already done I'm leaving is wrong 我出发了 means I (already) left 我吃了 means I (already) ate 他已经去过美国了 means he has (already) been to US
