Many common suffixes in English originate in Latin or Greek. Although others come to us second-hand from other romance languages, like French. -Able, for example (as in workable) comes from the Latin ibilis/abilis.
Suffixes are additions that are placed after a word. For example, for a suffix like '-ary' and a stem word 'legend', the result would be 'legendary'. Individual suffixes can be easily researched by looking them up in an Etymology Dictionary. Often, but not always, the suffix's origin is the same as the root word (philosophy is from the Greek word 'philosophia', meaning 'love of knowledge', and the suffix -y is from the Greek '-ia', meaning 'state/condition/quality').
Other Greek terms that exist as a suffix are -ist (artist, botanist, from 'istes', meaning 'one who does/makes'), and -ism/-asm (patriotism, enthusiasm, from 'isma').
The exact origin of a word or suffix can be tangled. For example, '-er' and '-or' (as in preacher or conductor) both correspond to the Latin suffix '-or' from 'orem', but probably come from the old English '-ere', meaning 'man who has to do with'. Complicating the matter is that English often borrows words whole-sale from other romance languages. These languages, however, also have roots in Latin and Greek. Thus, 'unique' is a French word, but the suffix ('-ique') is actually Greek ('ikos', meaning 'in the manner of/pertaining to').