Abarim Publications' online Biblical Hebrew Dictionary
The powerful and versatile particle ה (he) occurs as prefix and postfix:
(1) As prefix this particle predominantly serves as the definite emphatic article.
The noun בית (bayit) means house but the combination הבית means the house. The definite article occurs far less frequently in Hebrew than in English and is used predominantly to emphasize the noun it's stuck in front of (implying: this particular house).
Frequently, our prefix packs such demonstrative emphasis that it takes on the nature of substantive: הראה means 'the seeing' or 'those who saw' (Judges 19:30).
Hebrew has very few facilities to indicate possession; mostly the context is used to establish whether two nouns just sit side by side or whether one 'owns' the other. Often our prefix draws so much attention to its noun that it adopts this possessive function: the term צבא השמים (saba' hashemayim), for instance, means 'assembly of the heavens'. Still, technically, the possessiveness is implied and not explicitly expressed by the ה (he).
(2) Another function of the prefix ה (he) is as interrogative pronoun, basically to serve as question mark (that sits in front of a word instead of after). Connected to the particle of negation לא (lo'), it forms the term הלא, meaning 'is not?', with which many a question is introduced (Genesis 13:9). Another popular way to begin a question is to combine our particle with the particle of existence, יש (yesh), to form היש, meaning 'is there?' (Genesis 24:23).
As postfix this particle indicates (1) femininity, and (2) approach, which are closely related things according to Genesis 2:24.
The combination ביתה means either toward or into the house (Genesis 19:10), her house (Genesis 39:14), or the word house in a feminine form (perhaps 'housing'; Exodus 28:26).
Masculine words tend to denote things in their individual capacity or things that tend to exist solitarily, and feminine words tend to denote things that approach each other: that tend to cluster with other such things or are commonly known for existing as part of a group.