Some of the thoughts in here aren't up with paradigm change, economics for a starter, payload of 100 tons instead of 1 ton, that it's a private company with deep pockets doing it privately rather than a NASA mission and that it's not a one way mission that we used to think it was, so I'll have a go.
Financing is coming out of SpaceX, rather than NASA handing out money and it makes quite a difference. The NASA way doesn't happen as it is too expensive and all the rentseekers will leverage every last cent. SpaceX is building Starship without a NASA contract to do it (though it is subsequently providing a variant for the Artemis program). Some billionaires buy big yachts, this just happens to be Elon's version of a big yacht, ie something to do with the money that he finds meaningful. He is coming at this after a lot of lessons learned about high tech manufacturing, bleeding edge research and specifically, mass production and those lessons are coming into SpaceX, the speed at which they've been building prototypes at Boca Chica is astonishing. By comparison, the divisions of major manufacturing companies engaged in space aren't doing it as mass production, such as their airplanes, but it seems like after all these decades they still do it all bespoke.
The economics perception most people have about space colonisation is based on past endeavours. Space was expensive, that precious rocket or 2 and payloads for your venus probe or flag planting on the moon, was made harder and more expensive with the most cutting edge of everything to try and ensure success. So much unobtainium went into it, difficult/one off, extreme and barely tested materials and processes without a manufacturing base for it in existance and factoring in the rent seekers that made a fortune out of NASA and the military. What you all need to get your head around is Starship. A transformed space industry is Space Shuttle flying on average, 2.6 flights/year at $54,000/kg to orbit, to Falcon flying 1/month at $2700/kg to Starship at $10/kg, but mindbogglingly, they are aiming to manufacture starship at 1/week and (rapidly) reusable at that, which will mean many launches daily for cheap (not all bound for Mars). Yes that is an ambit claim by Spacex, how many they can build and the actual launch cost are yet to be proven. I've bought guitars online from Japan, I wish that I could get them via sea freight, let alone airfreight at $10/kg to Australia. To send 100 tons at a time (relatively cheaply) and with a fleet, instead of 1 ship with 2-3 astronauts and a measly 1 ton of cargo is a radical change from the 70s concept.
The key to paradigm change? Willingness to use good old fashioned steel instead of cutting edge materials and other common, well understood materials coupled with mass scale production processes instead of building unique items. Turned from an incredible science/engineering project that space was, into a mass manufacturing/engineering project. It is by comparison, going to a local engineering shop and getting them to design and make 1 car for me (which would cost a fortune) to buying a mass produced car. Similarly, the colonies themselves, if NASA made them, the entire habitat would be shipped from earth with the plumbing made from platinum (for reasons), after a suitable nanomaterial was devised for a chair in the loungeroom after a 10 year, 500 people research initiative involving 300 high tech companies and collaboration with international subcomittees on colour choice, chair height, east or west facing etc. The paradigm change will see them living out of Starship while they build the initial base out of an amount of material sent ahead, but will produce as much as possible out of locally avialable material. The space station has it's food and water sent up and the cost per meal is thousands, Mars will make it's own food and water. The cost per head for a trip to Mars according to one Musk soundbite was an intention to get it to a few hundred thousand dollars, for perspective the median house price in Australia is $693,000 usd. Sure, it is expensive, but not necessarily out of reach and fundible by proffesional individuals rather than the 1950s to 1970s concepts of manned missions to Mars which would bankrupt even the biggest world economies.
That reusable rocket will see Starships returning, empty or full, instead of having it's one use (meaning that it's only good for recycling at the destination). Even though the window to return is every 2 years, that you can return is radically different to it being a one way mission and is a difference in peoples inclination to go. Materials returning don't need to be booked at the full cost of a one way rocket from Mars to Earth.
The fundamental of why Mars vs elsewhere (aside from mother Earth).
It has the required, easy to get basic resources that let you resupply for the return trip. e.g. CO2 etc in the atmosphere, Water present in numerous places, means you can make the resources required for a return trip (fuel, oxidiser, food) which is why SpaceX is focussed on methane engines for Starship.
Those same basic resources of Carbon, Hydrogen and Oxygen let you make so many things, foods (proteins, fats, carbohydrates), plastics, petrochemicals, graphene/graphite. In instances, amounts of other elements are needed for variant compounds, but Mars has those too. When you do need specific things that organic chemistry won't let you do, such as a conductor for electronics (copper, silver etc), or Steel for construction and manufacturing, Mars has iron, carbon, chrome, vanadium, tungsten etc. But for the main part of construction and manufacturing, I think they'll get by quite simply with plastics and crushed rock (cement, bricks, concrete) for bulk building material plus conducting material, it will be made cheap and easy instead of the most advanced futuristic build, though that does not mean it has to be stone age living conditions.
Why would people go?
I've lived in multiple cities without a go home factor, home is where you make it, it's about why the destination is attractive. If you were an engineer, there are new challenges, almost any discipline of science would have people wanting new challenges, from the obvious in geology and vulcanology, to biologists researching foodcrops, new challenges for human bodies for medical, sports, new challenges for material sciences in different conditions (lower gravity etc). Also, people just needing a job, there will be opportunities for bartenders, service workers, farmers, miners etc. With the Starship program, ships will be returning be it empty or full, it's not like being sent for life to a penal colony, you aren't stuck - though you just can't immediately return on a whimsy.
That is a more specific and contemporary "why", but the same old "why" of migration still exists. How many religious colonies have been setup (oodles), ethnic migrations (oodles), opportunistic (from vikings settling the Faroe Islands, Iceland, Greenland, North America, Migrants from Europe to the colonies etc... Oodles). That's the people who want to go, then there are the people who will be sent, with Geopolitics on Earth being a thing, China, the States, India, Russia and others will vie for strategic positioning and send their soldiers, scientists and support staff.
Finally, it is not futuristic or fantastic, it is in progress now - the Artemis project by Nasa is about a permanent moonbase this decade and vast sums have already been spent, with the first launches to kickstart it off happening soon. Settling space is not the fantasy that it once was, but an active work in progress. It's just that, where NASA is focussed on the Moon, private industry (Spacex) is focussed on Mars and there is some crossover between the two.