Observation means to, "observe something or someone carefully in order to gain information", whilst inference means, "the act or process of deriving logical conclusions from premises known or assumed to be true."
So, put simply, inference is the summary of the information that has been collected. Observation is the act of gathering the information in the first place.
Observation can take place using all five senses. Using somebody cooking as an example, the observer will be able to see the food being cooked, they will be able to smell the food as it cooks, and hear the food sizzle. They will then be able to touch the food to ascertain its texture, and finally taste the dish. If someone were inferring something about the food, they would be commenting on the food after the event of the cooking process. Similarly if somebody were watching a sporting event or a concert, they would be observing it.
When they speak about the event to someone else, they are inferring that is was a good event or a bad event. The person inferring will be assuming that the person they are speaking to would have the same opinion as them, which is not always the case; different people have different tastes when it comes to most things. To sum up, observation will appear the same to everyone, as what they observe, using all the senses, will not change. Inference though is changeable, as it is often the opinion of different people.