A cognate is a word derived from the same root as another word. Cognates are words that have a common origin (source). They may happen in a language or in a group of languages.

Example One:
'composite', 'composition' and 'compost' are cognates in the English language, derived from the same root in Latin 'componere' meaning 'to put together'.

Example Two:
the word 'composition' in English and the word 'composición' in Spanish and similar words in French, Italian and Portuguese are cognates because they all come from the same root.

The general rule is that cognates have similar meanings and are derived from the same root (origin). A fine example is the word for night in almost all Indo-European languages:

nuit (French), noche (Spanish), Nacht (German), nacht (Dutch), nag (Afrikaans), nicht (Scots), natt (Swedish, Norwegian), nat (Danish), nátt (Faroese), nótt (Icelandic), noc (Czech, Slovak, Polish), ночь, noch (Russian), ноќ, noć (Macedonian), нощ, nosht (Bulgarian), ніч, nich (Ukrainian), ноч, noch/noč (Belarusian), noč (Slovene), noć (Bosnian, Serbian, Croatian), νύξ, nyx (Ancient Greek, νύχτα/nychta in Modern Greek), nox/nocte (Latin), nakt- (Sanskrit), natë (Albanian), nos (Welsh), nueche (Asturian), noite (Portuguese and Galician), notte (Italian), nit (Catalan), nuèch/nuèit (Occitan), noapte (Romanian), nakts (Latvian), naktis (Lithuanian) and Naach (Colognian), all meaning "night" and being derived from the Proto-Indo-European nókʷts ("night").

Basic English uses cognates, such as animal, attention, night, apparatus, experience, brother, invention, metal, etc.

History 
The word 'cognate' is derived from the Latin word 'cognatus' meaning 'to be born with'.

In reading Churchill's History of the English Speaking Peoples, it would be well to keep in mind (remember) what George Bernard Shaw says: "England and America are two countries divided by a common language."

Speakers of British English and American English face the problem of meeting false friends.

False friends 
As a rule, similar-sounding words have the same meaning but when they do not, they are called "false friends".

Example one: Spanish 'actual' and English 'actual' are cognates because they have the same root (origin) but they are "false friends" because Spanish 'actual' means "of the present moment" while English 'actual' means "real".

Example two: German 'hell', Norwegian 'hell' and English 'hell' are not cognates, but are spelled the same. In German, 'hell' means 'light' and in Norwegian it means 'luck', while in English it means hell.

False cognates 
Sometimes, two words look alike and it appears that they are cognates but they are not because they are not derived from the same root.

Example one: In the English language, the word 'light' (something that makes things visible) is not a cognate of the word 'light' (not heavy) because they are not derived from the same root.

Example two: The German word 'haben' and the English word 'have' mean the same thing and they appear to be cognates but they are not simply because they are not derived from the same root.

Example three: The Japanese word 'okiru' 起きる and the English word 'occur' have the same thing happening as example two.

Other websites 

List of words having different meanings in British and American English: on English Wikipedia
Common Spanish-English False Friends
German-English False Friends
French-English False Friends

References 

Linguistics