Do not give him your money at interest… (Leviticus 25:37)
Neither money nor food may be loaned at interest. (Food would be like, “Lend me 12 eggs and I’ll give you back 13 tomorrow.”) While these are both the subject of the same mitzvah, they are stated separately in order to express God’s great dislike of the practice. Since the Torah restates the prohibition, it reiterates the matter, which should serve as a disincentive.
The reason for this mitzvah was stated way back in Mitzvah #68, the prohibition against participating in an interest-bearing loan as a witness or a guarantor: a loan is supposed to help our brother out. He needs money and we’re in a position to spot him temporarily. By charging interest, it takes the transaction from the realm of “helping a brother out” to “profiting from another’s misfortune.”
Since this prohibition only applies to food and money, if you borrow someone’s car, it’s not interest to return it with more gas than it had when you received it. However, charging a lower amount if someone pays with cash instead of credit is a form of interest.
It is only prohibited to lend to other Jews at interest; one may charge interest when lending to non-Jews. This is because there is reciprocity in mitzvos. Since non-Jews are not commanded regarding interest, one may lend to them with interest and borrow from them at interest. Neither party has an inherently “upper hand” in the matter.
This mitzvah applies to everyone, at all times and in all places. It is discussed in the Talmud in the fifth chapter of tractate Baba Metzia, starting on page 60b. It is codified in Shulchan Aruch in Yoreh Deah 160. This mitzvah is #235 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #54 of the 194 negative mitzvos that can be fulfilled today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.