The Torah says that Paroh was nervous about Bnai Yisrael because of their increasing population (שמות א:ט). He therefore wanted to decrease their number, and he planned to do this in a wise way (שם פסוק י'). First he tried to crush them by forcing them into hard labor (שם פסוק י"א). When this failed, Paroh commanded his midwives to kill all male Jewish babies (שם פסוק ט"ו). The midwives, who were named Shifra and Pu'ah didn't do that at all; according to Rashi, Shifra and Pu'ah were actually Yocheved and Miriam. Paroh expected his wishes to be followed, but of course they were not. Once he realized that this plan was not working, he decided that all babies born, even to the Egyptians, should be thrown into the Nile River (פסוק כ"ב שם). Chazal say that Paroh knew when each baby would be born because he had a list of all the scheduled dates. Because Moshe was born early, as indicated by Rashi later (שם ב':ג'); his mother was able to put him into a basket which she placed in the Nile River.
We see from all of this that Paroh's various plans to destroy the Jews were foiled by Hashem. But not only did Hashem stop Paroh from decreasing the Jewish population, He actually saw to it that they increased in number. This happened because Hashem made many great miracles happen to help the Jews. For example, according to Rashi (שם א':ז'), the women gave birth to six babies at a time. This made the midwives unable to throw the male babies into the Nile. Obviously, it was Hashem's will that Bnai Yisrael should become numerous; no matter how hard Paroh tried, he could not stop it. This Parsha, then, represents the first "battle" between Paroh and Hashem; it would take Paroh much longer to finally realize that Hashem is greater and more powerful than he is.