Eight years of war against Iran had left Iraq deeply in debt especially to it's neighboring states including Kuwait. It also left Iraq with a very powerful army at that point in time considered roughly the 5th most powerful in the world. Saddam felt that the Arabian nations should have forgiven much of his debt because it was spent defending the primarily Sunni Arabia against the Shiite Persians.

Saddam had several goals when invading Kuwait.

The most obvious would be obtaining Kuwait's oil reserves which accounted for about 5% of the worlds total recoverable oil at the time. Controlling Kuwait would also give Iraq a true deep sea port to ship oil. Of course controlling this oil would also give Iraq a more powerful role in OPEC allowing them to more favorably control oil prices.

A second reason was to alleviate the debt. By conquering Kuwait Iraq immediately relieved debt owed to Kuwait. Invading Kuwait also sent a message to other nations that provoking Iraq (say trying to call in the debt) was a dangerous idea.

Saddam was also aware that at home he was not the most popular guy. He had been fought to a standstill against Iran. He had incurred huge national debt. There was still a Kurdish semi rebellion in the north and also fairly high unemployment. Before the Invasion Saddam spent over a year building a case against Kuwait to the people of Iraq. This allowed him to alleviate some of the problems such as unemployment by conscripting soldiers into his army. This also allowed him to shift some blame (The debt wouldn't be so high if Kuwait wasn't stealing our oil).

Kuwait made a good target because Iraq had a historical claim to the nation, Kuwait was comparatively defenseless, Kuwait was wealthy and Kuwait is located in a position where a major war could disrupt the worlds oil supply. Saddam counted on these factors keeping the Western Nations from interfering. Saddam knew he wasn't going to win a major war against the United States or even against a coalition of lesser nations. He was hoping that he could quickly take Kuwait and then talk the world down from a war.

In addition to iwinagin's excellent summary, it's worth noting that Saddam thought he had a green light from the U.S. to proceed. While they couldn't approve of the action, Saddam at least thought he had the Bush administration's assurance that they would keep out of it and limit their response to verbal condemnation.

This was based on meetings with U.S. Ambassador April Glaspie in the week before the invasion took place. Glaspie asked why Iraq was massing troops in the south, near the Kuwaiti border. Saddam said he was planning to settle their longstanding border dispute by force if need be and straight up asked what the U.S. thought about that. Glaspie's response was that the U.S. had "no opinion on your Arab-Arab conflicts, such as your dispute with Kuwait" and that the Kuwait dispute was "not associated with America."