If Kamala Harris steps in before the next election and runs for the next election, is that her 1st election or her re-election?

The US Constitution 22nd Amendment applies. It would depend upon WHEN she "steps in" about eligibility. It would be her first election, and may be her second and final term, or first term. This is very exact. If she has two or more years as President it counts as her first term.  

"No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of President more than once. " Passed by Congress March 21, 1947. Ratified February 27, 1951

Some history- 1) Nixon won in 1968. VP Spiro Agnew resigned, and Gerald Ford stepped into the VP role, never elected by the country as a whole. Nixon resigned after that, and Gerald Ford became the first President with no national level vote at all. Ford served as President August 9, 1974 – January 20, 1977, and ran for "first election" in Nov 1976 against Jimmy Carter and lost. Ford was never elected by the country, but we knew November 1976 was for his second term.

2) Lyndon Johnson was sworn in after the Kennedy assassination of  November 22nd 1963. He served November 1963 until January 1965 and then to January 1969 as his First full term. He chose not to run again.

The Amendment was added because of the more than two terms of FDR and his death April 12, 1945 when Harry Truman was sworn in. He served April 1945 to January 1949 as a term completing FDR's 4th term, and reelected in 1948 to serve until January 1953. Since the Amendment excluded the current President in 1951, he could have run again, but chose not to do so.

No US President has challenged the 22nd Amendment, but it is clear. More than two years is ONE TERM.   

First election.

Biden would have to pass away for her to be the candidate next time, and then she'd pick a VP. I think.

She's a bi-racial lawyer from California. I doubt the DNC is going to try to replace her, she's their ideal choice.

I'm so glad she's in the white house. There's literally nobody better to pull the sheets off of Trump's poorly concealed corruption.

Of course, his supporters are just going to whinge about 'fake news' but you know what my friends?

We NEVER have to listen to those inbred pieces of sh*t again.

Well, at least until america decides to elect another conservatard.