In more detail
On a loan, the principal is the balance you still owe excluding interest. Each month's interest is the rate times the remaining principal, and the rest of the payment reduces the principal, so in an amortising loan the principal part of each payment grows over time. Paying extra toward principal shortens the loan and lowers total interest, because every later month's interest is charged on a smaller balance; check that extra payments are applied to principal and not held for future payments. On an investment, the principal is the amount you started with.
Why it matters
Knowing the principal tells you what it would cost to pay a loan off today, and it is the base for interest, LTV and equity. A mortgage payment quoted as "P&I" covers only principal and interest; tax and insurance may be added on top.
Example
A $20,000 car loan at 6% over 60 months costs $386.66 a month. The first payment is $100.00 of interest and $286.66 of principal; total interest over the loan is $3,199.36. Adding $100 a month toward principal pays it off in 47 months with $2,444.38 of interest, saving $754.98.