Buddha, Dharma, and Sangha are known as the Three Jewels. When we go for refuge to the Three Jewels we enter into the Buddhist family.
Dharma is like medicine that prevents the sufferings of the three lower realms, Buddha is the doctor who gives us this medicine, and the Sangha are the nurses who assist us.
At present we are human and free from lower rebirth, but this is only a temporary and not a permanent liberation from lower rebirth. Until we gain a deep realization of refuge, we shall have to take lower rebirth again and again in countless future lives. We attain permanent liberation from lower rebirth by sincerely relying upon the Three Jewels.
Understanding this, we go for refuge to Buddha, Dharma, and Sangha.
More information on refuge, including a simple meditation, can be found in The New Meditation Handbook.