Scientists use this notation as an easy way to write really large, or really small numbers. A number like 108 represents 10 multiplied by itself 8 times, which is a 1 with 8 zeroes after it: 100,000,000.
A number like 10-21 represents 0.1 multiplied by itself 21 times, which is a 1 with 21 zeroes in front of it (including the one before the decimal point): 0.000000000000000000001.
This is frequently a much more efficient way to write numbers. For example, 3.765x1017 is much easier to write and think about than 376,500,000,000,000,000.