In Magic the Gathering, what is the point of fetch-land cards?

There's two things you gain out of it:

1) Depending on how many colors your deck has and how versatile the fetchland is, it allows you to get the color of mana you need to play a specific card you want to play *right now*. If you are running Black/White for example, and draw 3 Swamps, all white cards in your hand are dead cards. But if one of those Swamps was instead a fetchland instead, you could pull a Plains and have more options on what to play.2) It effectively is a 2-for-1 on using up lands from your deck. One of the biggest struggles with deckbuilding in Magic is that you need somewhere around 35-40% of your deck to be land in order to have a good chance of getting enough land in your starting hand, but most really good decks have little to no use for more than 5 or 6 mana in any single turn, so you very quickly get to where you *don't* want to draw land. Fetchlands pull lands out of your library, and therefore increase the percentage of cards left in your library that are *not lands*, aka, useful cards for combating your opponent.Also, don't focus too much on the loss of one or two life. The only life point that matters is your last one.

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I haven't played since '96 or so and then we had dual lands.  I used to wonder what was the point of dual lands since u still only got 1 mana out of them but then I realized they're good cuz u can replace 2 mountain and 2 forest with 4 tiaga in ur deck and if u get the tiaga then it's like either a mountain OR a forest.  They're just more versatile.

Later the dual land cards required a life point to use but the originals didn't.

The primary idea is to allow you to get the land that you actually need, especially in multi-color decks.  Additionally, some may allow you to fetch non-basic lands, meaning you can lay claim to a specialty card.  Finally, should the card reach a point where it is no longer necessary, it can be used as a throwaway sacrifice.

I think you meant sacrificing a land for a land right? If it's paying 1 life for a land, that's pretty nice to have because it's easy to recover life if you have the right spells.

1) They're handy in multi colored decks.

2) It reduces the library so that the next draw is unlikely to be a land card. Let's say you have plenty of land but no creatures. Reducing the library of lands increases your chance of drawing a creature, enchantment, instant, etc.