The Israelites had been traveling in the desert for about 3 months (which is a little longer than regular summer holidays) when they came to Mount Sinai. They were going to stay there for a while plus they excellent shelter from the mountain.
Moses got unpacked and decided to walk up the mountain to talk to God. Remember that this wasn't very easy for Moses, he was already over 80 years old.
God knew that Moses was coming so He spoke to Moses and told him to tell the Israelites to get ready. Moses came down to tell the people to have a bath and to clean all their clothes.
By doing this the people were getting prepared to hear important words from God. That is why we sometimes dress up or make sure we have clean clothes on when we go to church. It makes us hopefully behave a little nicer and shows respect to God.
On the third morning after Moses had talked to God, the Israelites where busy making their breakfast when all of a sudden there was a large rumble and a flash of light over the mountain. Anyone who was still sleeping were startled and woke up suddenly.
Everyone went out to look and just over the mountain there was lightning and thunder, and a very thick cloud hung over the mountain so you couldn't see the top. Even the mountain shook and the sound of trumpets could be heard getting louder and louder.
So Moses went up the mountain to hear from God once again. This time God told Moses, "Go down to the people and tell them not to follow you up the mountain, the mountain is a special place because I am here." So Moses warned the people not to touch or go to close to the mountain.