What is a power?
Powers are the little numbers you see written at the top-right hand corner of another number, e.g. 3² or 4³. We say we are raising the big number to the power of the little number, so we would read 3² as "three to the power of 2" and 4³ as "four to the power of 3". The big number is called the "base" and the little number is the "power".
The power tells you how many times to multiply the big number by the little number. So 3² = 3 x 3 and 4³ = 4 x 4 x 4.
Indices is just another word for powers. You will see both words used interchangeably in your mathematics textbooks and in BODMAS/BIDMAS. Indices is the plural, so you will see the word "index" to refer to just one power.
You may also see powers or indices referred to as "exponents". This is yet another alternative word, but it tends to get used more in America than in England.