In the TOS Bible, the Enterprise (and Starfleet) was referred to as "semi-military."
In Star Trek '09, Pike refered to "the Federation" as a "humanitarian and peacekeeping armada." - I am assuming that Pike meant *Starfleet* was a "humanitarian and peacekeeping armada".
And I've always liked that explaination of Starfleet's mission. How cool is that? I could be a proud to be a part of an organization like that. Could you imagine if the US (or whatever) military has "humanitarian armada" as part of it's mission description!?
Though I would amend that to "Humanitarian, Peacekeeping, and Exploration Armada".
And "Peacekeeping" involves fighting some times.
I suspect actually that over different eras and under different administrations and different political climates - both internal to the Federation and external to it, and even among different captains and admirals over the centuries, there has been an robust debate about what role Starfleet has in the Federation and what their focus "should" be.
Kirk in the rough and tumble 23rd centuries with "Klingons and Romulans hiding around every nebula" that he saw a more militaristic role - but he also gives the "Her 5-year mission" speech at the start of every show, which says it's "...to Explore Strange New Worlds, Seek Out New Life, New Civilizations, to Boldly Go Where No Man/One Has Gone Before..." - in other words, *exploration*. Nothing about "to defend to Federation, to kick ass, and take names...
AT THE SAME TIME...it's naive to ignore that Starfleet ships are HEAVILY ARMED (a single ship could blow an undefended planet back to the Stone Age, and glass much of it's surface.
And it's clear that Starfleet is the Federation's first line of defense in an invasion...and it's last line. And it falls to them to fight wars, such as the Dominion War, etc. That tradition predates the Federation. Plus the MACOS were folded into Starfleet, and apparently more than just "absorbed" but the MACOS mission ALSO became Starfleet's, as signified by the MACOS 5-pointed star thingy being put in the center of the Starfleet arrowhead/chevron emblem, according to "Enterprise". (I was disappointed when watching "Beyond" when the USS Franklin emblem just has some regular looking small 4-pointed star inside the chevron. Seemed to be a continuity gaff to me at first...but THEN just yesterday I noticed that same star shape in ALL OF the various MACO individual ship patches.
I do think the inconsistent quotes about the nature of Starfleet likely reflect an ongoing societal debate about what Starfleet *should* be.
ANYWAY...in *MY* "headcanon" Starfleet is...
"Starfleet is a Humanitarian and Peacekeeping Armada, the Exploration and First Contact Arm of the United Federation of Planets, it Represents the Federation, and it's Values, to the rest of the Galaxy. And we are the Federation's First and Last Line of Defense, Protecting it's Homeworlds, Colonies and Outposts, and Aiding our Allies when we are called upon.
THERE IS NO CALL WE WILL NOT ANSWER, NO TRUST WE BETRA...Ahay...oops, wrong franchise. sorry.
Anyway, WE ARE RANGERS, WE STAND ON THE BRIDGE, AND NONE MAY PASS, WE LIVE FOR THE ONE, WE DIE FOR THE...wait, I am doing it again...it's IN BRIGHTEST DAY IN BLACKEST NIGHT...
Uh...We Look For Things, Things To Make Us Go...
