"He likes ice cream."
Translation:Han tycker om glass.
Yes there are a few words for "think" that in English use the same word but have slightly different meanings. Most notably tänka - Thinking thoughts in your head / tycka - Thinking as in your opinion / tro - Thinking as in what you believe to be true. Tro also means "believe".
"Om" means "about" or "of" (it can also mean "if", but not in this context). "Tycker" means "thinks" in the sense of "has an opinion".
I don't know the exact origins of the phrase and I suspect it's just idiomatic. To make a little more sense of it you could look at possible modifications of it, for example:
"Jag tycker inte om honom", which means "I do not like him" or literally "I think not of him".
"Jag tycker mycket om honom", which means "I like him a lot", or literally "I think much of him".
Wow I posted this a while ago and I now know what om means. However you have enlightened me as this always seemed strange to me. I never thought of it but we actually say I think a lot of you which would mean like. We would never say I think of you to mean like though. Have a lingot for your late but incredibly enlightening response! ☺
I agree, skalpadda's reply has helped this phrase make much more sense for me. "I think a lot of her," or "I think little of him," would mean "I like her a lot," or "I don't like him much." It's archaic in English, and you don't hear it often, but people do still sometimes say things like "I think the world of you!" which means "I like you a whole lot!"
I love finding parallels like this, it makes "bridging" to a new language so much easier!