'By next Friday' refers to a deadline. It means 'on or before next Friday'. For example: 'This report must be submitted by next Friday'. This means that you can submit the report on Monday, Tuesday, Wednesday or Thursday if you want. Any time up to or including Friday is OK, but Friday is the latest day that you can do it. 'This report must be submitted next Friday' is different. This means that you must hand in the report ON Friday of next week. It is not possible to do this on any other day. Note that 'the next Friday' doesn't mean the Friday of next week. We use 'the next Friday' to refer to the Friday following another week. For example, you'd say 'I'm going to New York on August 3rd and I'm coming back the next Friday.'

By next Friday, I expect to have my work completed. This is to set a deadline either by yourself or by someone. By next Friday,....this will be accomplished. The next Friday is when he is arriving. This is just to refer to a day when perhaps a certain event will take place. Hope this helps!