For example, the term kilobyte has historically been used to mean 1024 bytes, and megabyte to mean 1,048,576 bytes. The multipliers 1024 and 1,048,576 are powers of 1024, which is itself a power of two (1024 = 2^10). It is this factor of two that gives the name "binary prefix".
This is in contrast to a decimal prefix denoting a power of 1000, which is itself a power of ten (1000 = 10^3). Decimal prefixes are used in science and engineering and are specified in widely adopted SI standards. Note that the actual prefix - kilo or mega - is the same, it is the interpretation that differs.
The 1024-based interpretation of prefixes is often still used informally and especially when discussing the storage capacity of random-access memory. This has lead to storage device manufacturers being accused of false marketing for using the decimal interpretation where customers might assume the larger, historical, binary interpretation.
In an attempt to clarify the distinction, in 1998 the IEC specified that kilobyte, megabyte, etc. should only be used for powers of 1000 (following SI). They specified new prefixes for powers of 1024 containing "bi" for "binary": kibibyte, mebibyte, etc.; an idea originally propsed by IUPAC. IEC also specified new abbreviations Ki, Mi, etc. for the new prefixes. Many other standards bodies such as NIST, IEEE and BIPM support this proposal but as of 2013 its use is rare in non-technical circles.
Specific units of IEC 60027-2 A.2 and ISO/IEC 80000
IEC prefix Representations Customary prefix Name Symbol Base 2 Base Base 10 Name Symbol 1024 (approx) kibi Ki 2^10 1024^1 1.02x10^3 kilo k, K mebi Mi 2^20 1024^2 1.05x10^6 mega M gibi Gi 2^30 1024^3 1.07x10^9 giga G tebi Ti 2^40 1024^4 1.10x10^12 tera T pebi Pi 2^50 1024^5 1.13x10^15 peta P exbi Ei 2^60 1024^6 1.15x10^18 exa E zebi Zi 2^70 1024^7 1.18x10^21 zetta Z yobi Yi 2^80 1024^8 1.21x10^24 yotta Y