"I can definitely understand going to nice beaches, warm weather, lovely cities, seeing sights, museums, art, wildlife, mountains etc. but I absolutely don't understand travelling for the sake of it."
I don't completely understand your question, people go traveling to do those things you've mentioned (plus additional points, like meeting people). People go traveling to see something new, experience something new. And you say yourself you understand why they want to do these things. If you're implying that most people go to a country to say they have been there, you are off the mark. Some do, but they're a minotity and traveling is something most people want to do when they're young, it's basically just finances that are stopping some.
I've lived in (and studied in) Spain, Scandinavia, France and London. I've traveled to most countries in Europe. You don't get a good impression of a city after one week of sightseeing and you certainly don't if you travel with someone from your home country or to a tourist-y spot. I like to learn different languages too, I want to visit the best bars & restaurants, I want to go to museums and see new exhibitions, I want to meet up with old friends I met in another country a long time ago and get introduced to their local friends. I want to, and have, established a network across Europe where I can go for a long weekend somewhere and have someone to meet up with. It's great. My life would be much less interesting without it. Fortunately, I have the finances for it as I have inherited money and have investments in my name back home. So I CAN go to Michelin-star restaurant or stay in nice hotels. Although I don't think that this is any way a prerequisite to travel, plenty of people stay in hostels etc and still have a great time.
There has always been a certain amount of snobbery around traveling, for some people. That changed as many airlines started to offer very cheap flights, so now basically anyone can go. I know some people who go to Hong Kong to explore on their own or to safaris in Tanzania and think that if you're European or American and haven't been to Asia or Africa, you're boring or not well-traveled. I find that attitude ridiculous - there are plenty of things to see in Europe and the US, and how far you travel is not a measurement of how adventurous you are. So yes, I think it's gone a bit too far for some, but it'll always be that way, and it is (fortunately) not the attitude most people have towards traveling.