Why is it taking so long to finish counting the votes in Arizona, Georgia and North Carolina?

It isn't taking unusually long. This happens every election. Please take a civics class.

Each state has different reasons.

In Arizona, the primary reason has to do with provisional ballots.  Since 2000, all states allow voters to cast a provisional ballot if there is a dispute about their right to vote.  In many states, including Arizona, there is a deadline for the voter to go to their election authority and present documentation supporting the right to vote.  To use an example, a person might have registered to vote five or six years ago and since got married or divorced.  If they renewed their driver's license after the marriage/divorce, the name on the driver's license might not match the name on the list of voters.  So they had to cast a provisional ballot, but the ballot will be accepted when they show up with their marriage license or divorce decree to prove that they are the person on the list of voters.  In Arizona, the deadline for presenting this type of documentation was this past Tuesday, November 10, and it looks like all of the small counties are done processing provisional ballots and will finish their count today (or already finished it) and the two largest counties will finish up their count tomorrow.

In Georgia, as others have noted, a recount has been ordered, so many of the counties are not updating with the provisional ballots now and, instead, will include those ballots with the post-recount vote totals.

In North Carolina, the deadline for receiving mail-in ballots was today (November 12).  I am not sure if it is a law or just a direction from the state election board, but the county election boards were not allowed to update their election night results until this deadline passed.  So, we will have all of the remaining votes announced within the next day or so.  (You have a similar situation in Ohio, but the election there is not close.)  

In all three states, the percentage is an estimate of how many outstanding mail-in and provisional ballots are left to count.  In a state like North Carolina, the estimate includes ballots that were mailed out but not yet returned.  (Eight states have not yet reached the deadline for receipt of mail-in ballots.  In all eight states, the ballot must be post-marked by November 3, but the laws give a cushion for potential delay in the mail.)  Because not all outstanding mail-in ballots will be returned and not all mail-in and provisional ballots will be valid votes, the real number outstanding is almost certainly less than the estimate.  

None of this is unusual.  California also has a large number of ballots left to count and will not finish up for at least another week.  But since California is not close for the state-wide races and control of the House rarely comes down to one or two seats, nobody particularly notices that California takes three weeks to count the vote (and the last part of the delay in California is that it has a really generous deadline for receipt of mail-in ballots reflecting that some of them are coming through international mail).  

Those three states are all about 99% done, meaning there are only some "provisional" ballots to be counted in those states, each of which needs to be carefully reviewed with official observers watching.

The only state that is well below 90% in their counting is Alaska, where because of state law they only started counting the mail-in ballots a few days ago.

The only state that has so far announced that they plan to do a recount is Georgia.

Georgia is doing a manual count.  PEOPLE looking at the ballots.
They started from scratch yesterday.  I don't know how people can be better than a computer but whatever.

I don't pay really pay attention to this so can't tell you what's going on in AZ or NC.
It's possible that it's takes awhile to open mail in ballots.

I don't think any start has certified the election. That usually doesn't happen until at least 2 weeks after the election.

Regardless of your viewpoint, we should all support this.  The California Secretary of State admits that there around almost a half-million bad ballots in CA.  This doesn't impact the Presidency but impacts local races, yet they aren't doing anything to fix it. 

unrelated to personal finance. I don't care and its not going to change the outcomes.