What is the translation of the word serre?
The sentence "La fille serre sa soeur dans ses bras" came up in my Rosetta Stone course, however they don't do any translating. Everything is done by pictures. From the pictures I assume that this sentence translates to "The women holds her sister with her arms" however when translated on Google translate it translates serre to greenhouse. I normally do not direct translate; however after 2 units of using this phrase I am still unsure as to its correct meaning.

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serrer quelqu'un dans ses bras = to hug somebody 
(http://dictionary.reverso.net/)

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Peachey is right: serre can be a noun, greenhouse
and also a verb: serrer (1st group) je serre, tu serres, il(elle) serre....

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Good guess! Obviously "serre" is the action of "la fille"(the girl; she), so we need to back-conjugate the verb to get the definition:

https://translate.google.com/#fr/en/serrer

"Hug" - serrer dans les bras - is the closest translation in this context.

You might have noticed that when Google translates "serre" as greenhouse, there are other suggestions at the bottom of the page, "serrer" being one of them.

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Hug indeed. Cela vient du verbe serrer, action de prendre avec sa main (on dit aussi "serrer la main", "serrer un livre"

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Or more generally "to squeeze," for example "lui serrer la main" -- in English, to "shake" his / her hand. "Serrer" is from a medieval Latin word meaning to lock (that is, to secure a door with a bar) -- whence the usual Spanish verb for "to close" --  "cerrar." The Italian "serrare" has a meaning between that of the French and Spanish cognates.