"This is my husband."
Translation:Detta är min man.
It's because when you say denna katt or detta bord, you're making a single reference to one grammatical entity. But when you say this is my husband, you're making two references to two grammatical entities, however unintuitive it may seem.
The detta is referring to an unnamed entity, and my husband is then bound to this entity through a process called anaphora resolution. In English, this doesn't really matter for how a human interprets the sentence, and it doesn't affect the grammar. But in Swedish, the unnamed entity is described as if it were a neuter noun, so you get detta är min man or det här är min man.
The sentence denna är min man is not ungrammatical, but it does not mean the exact same thing - rather, it would be like the English sentence this one is my husband, where you make an emphasis to show that it's not some other husband who belongs to you. And that follows another process.
As a test, you could turn the phrase around to see if it makes sense. For instance, you can say this one is my husband and you can say my husband is this one - a clear indication that you are making a single reference, and it should translate to denna/den här. But if you turn this is my husband around, you get my husband is this, which while not ungrammatical makes our brains complain, and so it should be detta/det här.
I realise this is hardly easy to keep in mind during casual conversation. To be honest, as a native speaker it's just one of those things I take for granted. If anybody has an easier rule to offer, I'd welcome it. (And by the way, the "it" in "it's just one of those things", follows the same rule and should thus be det in Swedish.)
And finally, if you happen to be a programmer, think of it like the difference between these two:
- public somevar; [...] somevar = 42; // creates a placeholder variable, later makes it an integer at assignment
- public int somevar = 42; // immediately creates an integer with a given value
rwhodges is right. The difference between detta and det här only surfaces when they stand together with a noun. When there's a verb between the demonstrative pronouns and the noun, it's no longer the demonstrative pronoun that decides whether the noun is definite or not.
Jag vill ha den här bilen 'I want this car'
Jag vill ha denna bil 'I want this car'
Den här bilen är min 'This car is mine'
Denna bil är min 'This car is mine'
Det här är min bil 'This is my car'
Detta är min bil 'This is my car'
'this' in the last two sentences doesn't directly refer to the car: rather, it refers to 'the thing I'm talking about'.
I'm sure Arnauti can explain this better but consider the differences between the sentences Det här huset är mitt and Det här är mitt hus. "This house is mine" versus "This is my house". I guess it's that when you say "this X" you use the definite form, but when you say "my X" you use the indefinite.