I have a Jewish mother and a Christian father. What am I?
"I understand that my Jewish faith comes by way of my mother and not my father. If this is true, why do we trace our heritage through Abraham and not Sarah? I have a Jewish mother and a Christian father. What am I?"
As you may know from watching the news, the issue of who is a Jew is a hotly debated one nowadays. There is no simple answer.
Traditionally, the definition is a double one. Your status as a Jew depended on the status of your mother: if she was Jewish you were Jewish and so on. But your tribal affiliation (Priest, Levi, Benjaminite, Judean,...) was determined by the father. Why matters evolved this way is entirely unclear. These laws as such are spelled out fully only in the time of the Mishnah (around 230 CE). It is not necessarily the case that these laws were in operation in just this way back in Biblical times, let alone the time of Abraham. The question is moot in any case since both Abraham and Sarah were "Jewish."
In 1983, the Reform Jewish Movement decided that it would accept as Jewish anybody who has one Jewish parent (i.e. mother or father) and who was raised Jewishly. This policy of "patrilineality," as it is called, is one of the points of disagreement between traditional and Reform Judaism since some people can now be considered Jewish by one movement but not the other. If the person in question is a woman, then the disputed status would presumably be carried forward into the next generation, etc.
As to your case, because your mother is Jewish, you would be considered Jewish according to halacha (Jewish law), and so by all Jews (unless you openly declared otherwise). If you consider yourself a Christian, say, and act accordingly, then you would be considered a Christian by Reform, but still Jewish by Orthodox standards.
In the end, there is no universally agreed upon answer among Jews, and in some cases other groups have other answers entirely.