Debits and credits, and the technique of double-entry accounting, are credited (no pun intended) to a Franciscan monk by the name of Luca Pacioli. Known as the "Father of Accounting", he warned that you should not go to sleep until your debits equaled your credits.
Let's review the basics of Pacioli's method of bookkeeping. On a balance sheet or in a ledger, assets = liabilities + owner's equity. An increase in the value of assets is a debit to the account, and a decrease is a credit. On the flip side, an increase in liabilities or owner's equity is a credit to the account, and a decrease is a debit.
Having Latin roots, the term "debit" comes from the word "debitum", meaning "what is due", and "credit" comes from "creditum", defined as "something entrusted to another or a loan". So when you increase assets, the change in the account is a debit because something must be due for that increase (the price of the asset). Conversely, an increase in liabilities is a credit because it signifies an amount that someone else has entrusted (loaned) to you and which you used to purchase something (the cause of the corresponding debit in the assets account). You can see why simply using "increase" and "decrease" to signify changes to accounts wouldn't work: the terms "debit" and "credit" signify actual accounting functions, both of which cause increases and decreases in accounts, depending on the type of account.
What about the terms' abbreviations? There are a few different theories as to why debits are abbreviated "DR" and credits abbreviated "CR".
One theory asserts that the DR and CR come from the Latin past participles of debitum and creditum which are "debere" and "credere", respectively. Another theory is that DR stands for "debit record" and CR stands for "credit record". Finally, some believe the DR notation is short for "debtor" and CR is short for "creditor".
The approach Pacioli devised has become the basis of modern day accounting, and the use of debits and credits allows companies and individuals to keep track of their transactions and manage their money. While the origin of the abbreviations of debit and credit (DR and CR) remain somewhat of a mystery, each theory has "credibility".