[Moshe] cried to Hashem, and Hashem showed him a "tree", and he cast it into the waters, and the waters were sweetened.
There He made for them a statute and an ordinance, and there He proved them, and said: "If you listen carefully to the voice of Hashem your God, and do that which is right in His eyes, and listen to His commandments, and keep all His statutes, I will put none of the diseases upon you which I have put upon Egypt, for I am Hashem who heals you." (15:25-26)
The word "diseases" is probably a reference to the plagues, though most of the plagues did not seem to directly involve disease. (Although who knows - with all the bugs flying around and the frogs and the bad drinking water, not to mention the plague and the [smallpox?] boils, many of the plagues might have led to sickness of some sort or another.) But why would God need to reassure the people that they would not receive plagues just as the Egyptians did?
In the story to which God's promise is a reaction, the only drinking water available to Bnei Yisrael was salty, and Moshe had to miraculously make it drinkable by throwing in an "tree" ("etz", i.e. some unknown wood thing). This scene bears an striking resemblance to the plague of blood. There too Moshe miraculously changes the water's potability by striking it with a wooden implement (his staff).
Did Bnei Yisrael notice their current lack of drinkable water and associate it with what the Egyptians had gone through in the first plague? Did they perhaps think the 10 plagues were being more or less repeated, now with them as a target? The obvious difference between the two parallel "plagues" is that Moshe made the Nile undrinkable, while now he made the spring drinkable. But assuming the people feared a new set of plagues, Moshe's use of the "tree" would be a carefully chosen gesture, designed to confront the people's fear and show it was unreasonable. Then God would formally promise not to repeat the plagues, and hopefully all irrational fears would be taken care of.
Thus everything works out neatly, except for the obvious question: why on earth would the people fear further plagues in the first place? I can think of two possible reasons. First of all, they had already complained several times to Moshe, and possibly doubted his and God's authority. While this is not yet explicit in the story, we know that not too long will pass before they openly rebel, and even before that it must have been clear where public opinion was headed. Thus, they had reason to expect punishment. Egypt received the plagues because it refused to recognize God's role, and now Israel was denying God's role? Not a good situation.
Alternatively, (some of) the people may have had a woefully unsophisticated theology. In the ancient world it was believed that different natural forces were controlled by different gods, and I'm no expert, but it seems reasonable to assume that some gods were considered "helpful" and others "dangerous" and to be stayed away from. If some of the Israelites thought this way, they might have come to the conclusion that God was a "destructive plague god" whose role was to terrorize whoever was in his midst. So far Egypt had absorbed all the punishment, but with such an out-of-control deity, in whose "territory" the people were now located, it looked like they were the next likely target.
Either way, it would have taken Moshe's demonstration as well as God's promise to convince Bnei Yisrael that by obeying from now on, they could avoid the terrible punishments they had recently seen.
I know this interpretation is interesting; I don't know if it's reasonable.