In computers, we tend to talk in three bases, binary (base 2), decimal (base 10 - the one you are familiar with), and hexadecimal (base 16). Computers usually encode everything in binary digits
A bit is b-inary dig-it - a digit in base 2 that is either a 0 or 1. E.g., you could represent the decimal number 42 as 6 binary digits: 101010bin as 42 = 32 + 8 + 2 = 25 + 2 3 + 21.
Similarly every hexadecimal digit is a number between 0 and 24-1= 15 = fhex = 1111binary. The 16 hex digits are 0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f. (Sometimes the last 6 characters are written in uppercase -- its the same letters).
So if you see a hash that looks like
b1946ac92492d2347c6235b4d2611184 you can immediately notice that there are 32 hexadecimal characters. Thus as every hexadecimal character is 4 bits, it is 32*4 = 128 bits.
While we are at it, should mention that a byte is a convenient unit -- most plaintext characters in a text file are represented in one byte of data; e.g., a 100 kilobyte plaintext file will have about 100,000 characters in it. A byte is 8 bits - in binary a number 0 and 255 = 11111111binary = ffhex) - two hexadecimal characters.