“These do look good for a mobile phone.”
You're looking at photos on your friend's new mobile phone. Your friend mentions how impressed he's been with the quality of the photos that the phone takes. You say this in agreement.
These do look good for a mobile phone.
In a normal sentence, you don't include "do" before the verb:
These look good for a mobile phone.
But you can use "do" for emphasis in sentences like the one above. In this case, the speaker says "these do look good" instead of "these look good" because he's emphasizing that he agrees with the speaker. You can also use "do" in this way when you're saying something different from what you or another person just said:
I'm not a big fan of the current prime minister. I do agree with him on defense, though.
In these sentences, you place a strong stress on the word "do".
This kind of expression is used when you want to compare how good something is with other things of the same type. In the example above, the photos that were taken with the mobile phone probably don't look very good compared with photos taken by a professional photographer on an expensive camera. But they look better than other photos taken on mobile phones.
This type of phrase can take lots of different forms. The verb doesn't have to be "looks". It can be "sounds", "tastes", "is", and other verbs. This can be followed by "good", "well", "strong", "small", or any other adjective. Here are some examples:
You throw pretty well for a girl.
That tastes really good for something you just made up yourself.
He's smart for a dog.
Notice that the example at the top is used in spoken English. It's not quite grammatically correct because "mobile phone" is not the correct category for "photos". A more grammatically correct way to express this in written English would be:
The photos he showed me looked good for photos taken with a mobile phone.