The abstract is written for the potentially interested reader. While writing it, keep in mind that most readers read the abstract before they read the paper (sounds obvious, but many abstracts read like the authors did not consider this). The abstract should give an impression what the paper will be about. Do not use jargon or any abbreviations here. It should be understandable for non-specialists and even for people from fields somehow far away.
The conclusion should conclude the paper. Keep in mind that the most readers have read the paper, when they read the conclusion. Again, this sound obvious but, again, a lot of conclusion do not read like this. It does not make sense to write a conclusion like "we have shown this and that by using this and that method". Well, this is what the read has just read. A proper conclusion should tell the reader what she can or could do with the newly acquired knowledge. Answer the question "So what?".
A summary sums up the paper. I am not sure if a paper needs a summary.
I've written some tips for abstracts some time ago:
Avoid jargon. Although this sounds obvious, most abstracts contain jargon in one way or the other. Of course one can not avoid the use of specific terminology and technical terms but even then there is an easy check, if a technical term is appropriate: Try to find a definition on the internet – if you do not succeed within a few minutes you should find a different word.
Use buzzwords. This may sound to contradict the precious point and in part it does. But beware that you can use a buzzword together with its explanation. Again, the example from the previous point works: “Funk metric” may be a buzzword and the explanation using the name “Finsler” is supposed to ring a bell (as I learned, it is related to Hilbert’s 23rd problem). This helps the readers to find related work and to remember what was the field you were working in.
General to specific. In general it’s a good advice to work from general to specific. Start with a sentence which points in the direction of the field you are working in. So your potential audience will know from the beginning in which field your work is situated.
Answer questions. If you think that your work answers questions, why not pose the questions in the abstract? This may motivate the readers to think by themselves and draw their interest to the topic.
Don’t be afraid of layman’s terms. Although layman’s terms usually do not give an exact description and sometimes even are ridiculously oversimplified, they still help to form a mental picture.