Hamlet says this in Act 1, sc. 2, during his first major soliloquy. He is speaking about Gertrude and the line means, "I don't want to think about this. Women are weak-willed!" He means that he is so upset that his mother would not only remarry so quickly after her husband's death, but that she would marry Claudius, her dead husband's brother. Hamlet clearly does not care much for his uncle. When he compares his uncle to his father, he describes his uncle as a "Hyperion to a satyr" (6 lines before the line you quoted). Hamlet cannot see what his mother possibly sees in Claudius. Added to both of those deterents to the marriage between Gertrude and Claudius is the fact that, in the eyes of many, Gertrude committed incest by marrying her brother-in-law. In those days, many felt that when a woman married a man, she became part of his family to the degree that his siblings became her siblings, so she was marrying her brother in the view of those believers.
This quotation comes from Hamlet's first great soliloquy in Act 1 scene 2 in which he rails against his mother's unseemly haste in re-marrying his uncle after his father's death.
I would firstly discuss the importance of this as being part of a soliloquy in which Hamlet expounds his thoughts directly to the audience rather than to another character.
The fuller context is:
"... and yet, within a month--
Let me not think on't--Frailty, thy name is woman!--
A little month, ...--married with my uncle"
It is important that Hamlet is unable to think about the speed with which Gertrude has re-married: it is the "within a month" which prompts the "Let me not think on't". This suggests that he is so disgusted with her that he cannot comprehend it at all.
The quotation shows a personification of the concept of "frailty" - by which Hamlet means fickleness and a lack of faith, a spiritual rather than physical weakness.
It also shows a generalisation of his anger: it is not simply Gertrude who is frail but "woman" suggesting a (to modern ears) unpleasant mysogyny which also comes out later in his conversations with Ophelia.
I would also point out the exclamation mark and caesura in the quotation. These break the flow of the poetry and grammatical structure indicating Hamlet's mental instability and fractured psychology, a feature of the entire soliloquy.