Rolling your scores is a quintessential part of making your character. It's up to you...or more accurately, the dice...but what
you roll for
your character.
I will also throw my hat in that I have never been in a "point buy" system. Though I have been in the "-2 from one ability to +1 to another" to, hopefully, mesh out the character class/concept you, may have, originally conceived/wanted.
For rolling/generation styles:
I've done 3d6 in order and 3d6 place as desired.
I've done 4d6 drop the lowest (most often), both "in order" and "place as desired."
And, as noted, have used the -2/+1 swap (was that an "official" optional RAW? I'm thinking it was, but can't really definitely remember now) in just about all of those.
I'm all for the 5e offering all of those as optional/possible ways of generating abilities. To make a "This is how" proclamation, seems unnecessary to me. Give them 4 or 5 options and let the DM pick. Hell, through in a "point buy" option as well. Everyone gets [to choose] what they want!
For the "what" of the ability scores, we always interpreted things as such:
Strength: physical strength. Everone's got this one covered/under control. How hard you hit, how much damage you do, can you break down the door?, can you hand onto the rope? swim across the channel? lift/carry lots? Your actual physical "build"...which then would/should influence others to a degree (intimdation, physical attraction, etc.) You shouldn't have a "thin, frail looking guy" with an 18 strength (assuming 18 is the top pinnacle of human physical strength). I don't care what race he is, a guy (or girl) with 16, 17, 28 (!) Str. is CUT, bulky and
ripped dowwwwwn!
Constitution: endurance...the ephemeral "fortitude". Can you stave off disease? Conquer the poison coursing through your veins? Yes, "hold your breath". Survive trailing Merry and Pippin for 3 days without needing a break to sleep or eat? You can be "physically weak" (low Str) but "tough as nails." (high Con)
Dexterity: can you move quickly, precisely, accurately? Can you aim your bow or get that sling stone to land where you want? Dive aside of the incoming dragon breath in time? Better AC, better to hit with missiles, better "Reflex saves".
Intelligence: your "smarts". Can you learn that language or this spell? How many? Can you put together different elements in a coherent logical fashion and get the proper results/outcome? Can you
remember what it is you once learned? All "cognitive" functions. A "Spock" character as easily as a "Rainman" as easily as a "fictional character I can't think of right now who is just STUPID smart but not at either of those extremes." [EDIT] OH! Came up with one down post, Dr. Brennan from Bones! [/EDIT]
Wisdom: I would say how "enlightened" are you, instead of or in addition to how "aware" you are. How well you can make solid "good" decisions for your character..."Common Sense" if you will. (Note: I feel the player's awareness/knowledge and "common sense" always needs to take a back seat to the Character's Wisdom/"common sense"!). More importantly, for the divine types, how strong is your faith? Your connection to/understanding of your "divine" (thence, your "bonus" spell capacity). Reading and connecting with "emotion" (empathy). And understanding, in general of "emotion" vs. Int's "understanding" of facts. [For an EXCELLENT take on this, watch the tv program
Bones. Temperance Brennan is an excellent example of Int. without Wis.] Your power of personal will (moreso than "Charisma", though I definitely see them as connected in this event) to overcome things...hence, Will saves. One's "gut feeling". Facilitating "Soul", if I can make that distinction, vs. Intelligence's facilitating "Mind".
Charisma: Your "personality" and your "like-able-ness." Your capacity to influence others, moreso than your "Wisdom". For most, and myself, your "looks" are wrapped up in this.
In my learned opinion (note, that is "learn-ed" not "learned"

) Charisma is, by far, the weakest link. Easily subsumed by Wis and Int, other than the physical appearance of folks...which could be wrapped up in Strength (And thence came "Comeliness" and thence, but for the grace of Wee Jas, it went)
But then, they added/made things like Sorcerers (though I don't know realyl any of the "rulz" about them, I have gathered they cast on/dependent on their Cha) and Bards' casting dependent on Charisma (makes sense), the "interaction" skills, and the paladin (and I forgot until recently, the DRUID!) already had a HUGE Charisma "requirement" to be the classs...I think the ranger, originally (in 1e) also.
So, then, Charisma couldn't necessarily be the "throw away" ability score anymore.
Anywho, I like 'em all. All 6. They all have a place in defining the physical, mental and otherwise ephemeral qualities of your fictional character. I want/hope they all stay and want/hope they all keep their "traditional" functions.
--SD