The verbs 'look for', 'seek' and 'search FOR' are all similar in meaning.
1. 'Look for' is the normal, everyday expression which we use when we are trying to find something. For example
'What are you doing?'
'I'm looking for my keys. I can't remember where I put them.'
'Can I help you, sir?'
'Yes, I'm looking for a present for my aunt'.
2. 'Seek' is more formal and old-fashioned. You might find it in a written advert, a poem or a proverb. We don't tend to use it in everyday speech.
3. 'Search for' suggests that we have to look through many things before we find what we want. That's why we use it for internet searches - we have to go through a large amount of data to find the internet page we need. Or, for example:
'I spent all morning at the library searching for the right book.
NB Note that the verb 'search' on its own has a different meaning. The object of the verb 'search' is the location where the searching takes place. For example:
The police searched his house trying to find evidence.
The customs officer searched his bags looking for drugs.
I hope that helps.