You make an inference when you combine a new observation with what you already know to form a conclusion. This is how a hypothesis is generally formed. You observe something new, for instance, you observe that ants only leave an ant hole during the day. You know from science class that the ants that leave the ant hole are looking for food. You infer that food can only be found by ants during daylight.
Inference is generally the process used in forming a hypothesis and it combines something you observe with your previous knowledge.