Chapter 17 of The Scarlet Letter is about the reveal that Hester makes to Dimmesdale regarding the true identity of the man who Dimmesdale knows as Chillingworth. Hester's guilt over this matter drives her to ask Dimmesdale for forgiveness over and over. His answer is that he does forgive Hester, however, Dimmesdale reverts to the fact that both he and Hester have also committed a flaw. Yet, he concedes that no matter how badly he and Hester have behaved in the eyes of society, their "sin" was not evil, nor intended to hurt others. Chillingworth's sin, however, was intentional and mean.
This is when Hester agrees with Dimmesdale and says the words
What we did had a holiness of its own. We felt that! We told each other so. Have you forgotten that?
By "consecration", Hester refers to the holiness that entails the act of procreation, particularly when both parties are seriously committed to each other's love.
However, if you notice the need for Hester to say "Have you forgotten that?" denotes that there is an underlying problem in the relationship between Hester and Dimmesdale: Arthur has obviously forgotten it, which is the reason why Hester feels compelled to re-instate the difference between the evil intentions of Chillingworth and the love that comes out of a true romance.
Somewhere in the larger scheme of things, Dimmesdale seems to have refused to commit his relationship with Hester to memory. As a result, he fails to make the instant connection that would help him to understand that, if he looked at things from a completely different perspective, he would stop thinking that bearing Pearl is a sin. Instead, he would perhaps see for once that what comes out of love is never a sin.
This leads us to wonder then: was Dimmesdale acting out of love, or out of lust, when he and Hester got together? Is Dimmesdale hiding from, both, Hester and the reader, the fact that he has another secret? The secret that he never really loved Hester in the first place?
This explains why he keeps a distance from Pearl; it also explains why he is never finite with Hester as far as their plans go; it may also be the reason why he continuously colors his relationship with Hester as a sin. It was a sin, but it was his own to that matter: the sin of lust, and the sin of lying to Hester from the get-go regarding his true feelings for her.
This information may very well be extrapolated from the phrase, as it clearly shows that there is insecurity and wonder from Hester's part.
Many Hawthorne critics believe that Hester's beliefs about independence were based on the beliefs of the New England Transcendentalists. They believed that human nature was basically good. They believed that society was a corrupting influence. The Transcendentalists believed that a person should follow their highest natural impulse even if it brought them into conflict with their family and society.
So, in Hester's case, the "consecration" she refers to could very possibly be her own free nature. The passage quoted takes place in the woods, a place of nature outside of Puritan society. Hawthorne associates Hester with Nature in other parts of the book. A good example is the rose bush outside of the prison, which Hawthorne associates with Nature and another feminist rebel, Anne Hutchinson.
The rose bush symbolizes Nature, or individual wilfullness, and it contrasts against the prison house, which symbolizes social convention and conformity.
Hester follows her own higher nature in her love for Dimmesdale and her refusal to expose him as her lover. Anne Hutchinson followed her higher nature in rebelling against their beliefs of the Puritans. In both cases, both women--like wild roses--sprouted up in rebellion against Puritan society because they felt that their beliefs--their highest natures--had a "consecration" of their own. For them, Nature has a higher authority than social custom.