The name sounds fancy, but really the concept is simple. Most corpora are monolingual, but with parallel corpora, the texts have been translated so when you search for a term in one language, you can see the way that word has been translated into the other language(s).

If you want to play around with this, the link is http://www.let.rug.nl/~tiedeman/OPUS/.

Here is an example of searching for the English word ‘honey’ in TURkish:

tur
220 tatlım
29 hayatım
17 canım
14 Tatlım
5 Hayatım
4 bal

Now, if you click on a number beside the term you are interested in, you will get a listing of the original English text with ‘HONEY’ and the translation of that text.  In this case, I clicked on ‘14′ to see how ‘Tatlim’ appeared with the English translations (from movie subtitles):
12162141 Oh , honey , you were incredible .
tur - Tatlım , müthiştin .
14931248 - Honey , honey .
tur - Tatlım , tatlım .
15944691 - honey , let’ s go .
tur Tatlım , hadi gidelim , hadi gidelim , hadi gidelim .
16975602 Oh , honey , he was trying to save his pet .
tur Tatlım , hayvanını kurtarmaya çalışıyordu .
16983418 Hey , honey .
tur Hey , Tatlım !
16988175 That was sweet , honey .
tur Tatlım bu çok hoş .
17994433 Honey , honey , here .
tur Tatlım , tatlım , buraya koy .
25470953 I’ m so proud of you , honey … being out in the world like this .
tur Tatlım , seninle gurur duyuyorum — böyle bir dünyaya çıkışınla .
25471594 I’ m just waiting for you , honey .
tur Tatlım , ben sadece seni bekliyordum .
28966134 Honey , honey .
tur Tatlım , tatlım .

Also, if you click on any word in one of the foreign languages, you’ll see a list of the possible translations in English.  In this case, this is how Tatlim maps into English:

eng
220 honey
56 sweetheart
51 dear
51 sweetie
14 darling
8 baby
7 Honey
7 hon
2 now
2 Sweetheart