The phrase 'I'd like...'

Merhaba!

This morning at heritage language class (a.k.a. 'Hungarian school' (even tho'
of the hundred(?) or so students, only about 30-40 are Hungarian)), I was
writing out vocab when I noticed that, when we got to it, the phrase 'I'd
like...' is idiomatic. Here's the sentence taken apart:

I = 1st person singular nominative personal pronoun(! :) )
'd (<- would) = cliticized conditional mood auxiliary verb (right?)
like = think favourably of, enjoy (1)

So doesn't 'I'd like...' really mean 'I want (polite - with Japanese -masu)'?
If so, what's a conditional mood doing modifying a verb meaning 'to think
favourably of (1)'? Shouldn't it be 'I wish to have (take possession of)...'
or 'I'd appreciate it if you gave me...'?

Could someone explain this weird construction to me?

(1) I've also noticed that 'to like' can also mean 'to enjoy X', as in 'He
enjoyed the game'.

--Trebor

PS: It's actually [tREboR].

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