I testify that there is no god but God, and I testify that Muhammad is the Prophet of God.
The shahadah consists of two statements uttered in a single sentence. The first statement, no god but God, is the Muslim's testification of pure monotheism. We attest that there is no person or thing that is worthy of worship other than God. There are not multiple gods, nor is there anyone or any thing that shares godhood with God. Thus, Muslims reject, for example, the concept of the Christian trinity and the Hindu/Buddhist pantheon of gods. Likewise, we reject the atheist's assertion that there is no god at all. There is only one God, solitary and unique (ahad). To believe in these other concepts is to commit shirk, the one unforgivable sin.
Say: He is Allah, the One!
Allah, the eternally Besought of all!
He begetteth not nor was begotten.
And there is none comparable unto Him.
- Surah Al-Ikhlas (The Unity), 112:1-4, Pickthall translation
The second statement, Muhammad is the Prophet of God, has several connotations that need to be considered. First is the face-value statement acknowledging Muhammad's (pbuh) prophethood. A Muslim could very easily acknowledge the other 24 named prophets (pbut) in the Qur'an in addition to all the thousands of unnamed prophets, and this would be stating the truth. But, by acknowledging Muhammad (pbuh) as a Prophet, we are binding ourselves as Muslims to obeying Islamic law and jurisprudence (shari'ah and fiqh, respectively) as best we can.
The shahadah occupies the first pillar of Islam because of its importance and the frequency with which it is said. In a normal day, a Muslim will recite the shahadah at least nine times throughout the course of the five required prayers; this does not count all the other optional prayers a Muslim may make on any given day. Nor does it count any other time the shahadah might be spoken for other reasons.
The shahadah is also important because it is the normal standard by which people are recognized by the Muslim community as a fellow Muslim. A new Muslim must recite the shahadah publicly (defined as in front of at least two other people) and they must do it with sincerity in their hearts. Simply reading or reciting the shahadah above will not make you a Muslim if you lack sincerity, nor will other Muslims recognize you as a Muslim if you do not say the shahadah at least once publicly. You might be a Muslim in your heart, but that does not necessarily mean public acceptance.